← AMRAL · BSD 猜想 · 第二層

BSD 猜想 · 獨立重算線

這條線對 AMRAL 的 BSD 研究做獨立重算：每一個有限主張用自己的程式重算、每一份文件按它自己的標籤讀、每一輪一份報告與一個可重跑的 gate，整棵樹的 gate 每輪都經過突變演練（種入缺陷，要求被具名的檢查抓到）。這裡的每個狀態只有 PASS / OPEN / UNMEASURED，沒有「證明了」。

第一層（探索頁面）：BSD 猜想。這一頁是它的驗證紀錄。

狀態帳本

以最新一輪的 package 為準 · RUN-107

normalization_certificate CLOSED (architecture), frozen BSD OPEN DAG A PASS (cited-theorem route) B PASS C PASS (C_NT PASS, C_p PARTIAL) D PASS E-G untouched

這條線自己劃的界線：BSD OPEN. The normalization certificate C1–C10 is CLOSED as architecture and frozen (RUN-102); the post-normalization DAG stands at A PASS by cited theorem (RUN-104), B PASS (RUN-105), C PASS (RUN-106), D PASS (RUN-107); E–G untouched.

演練

整棵樹的突變演練，最近一次

218檢查
692種植缺陷
687被具名檢查抓到
179控制組不動

種植缺陷 692 ＝ 被具名檢查抓到 687 ＋ 由崩潰偵測到 5；後者不算「被具名檢查抓到」。

回合表

每一輪：主題、gate、摘要（做了什麼 — 判定） · 110

回合主題gate摘要
001where the corpus actually livessrc0085 curated docs on the site, 292 in the tree; four locations reconciled by content hash
002certificate-ladder vocabularysrc01rung usage across all 85 documents
003the route Phase 0 rejectedsrc02the lattice-point rank idea does not recur after its own audit
00440,749 discriminants, 135,787 valuationssrc04recomputed; the fourth check reported vacuous rather than passed
005a₃ over F₃, all 4,062 removed curvessrc05a bucket was holding two kinds of number
006the 3-isogeny columnsrc064,062 of 4,062, and two errors of mine caught by a second derivation
007the 5- and 7-isogeny columnssrc07, src08all 12,186 determinations decided both ways via X₀(n); zero disagreements
008the 36,687 curves the census keptsrc09the direction the census's own checks are blind to; and the base is two populations
009Phase 2 Theorem 1.1(1)src10the density is 1/24; the obvious answer 1/48 is wrong
010this arm's own gatessrc1127 defects / 27 caught by the named check — after the first run caught only 24
011P5 — 389.a1 at p = 11src12the v1.1 localization matrix [[1,2],[1,4]] recomputed from scratch, det 2 ≠ 0
012Algorithm 2's twist mapssrc13, src11all 247,391 twists rebuilt, 36,687 of 36,687 lists exact; a docstring that contradicts its own code
013Phase 0's Certificate Globalizersrc14all four claims hold in ℚ; the faithfulness fails in float64 at a computable index
014the Phase 2 anchor, 696.e1src15N = 696 and r_an = 0 both computed; L(E,1)/Ω = 1 to one ulp
015Theorem 1.1(2) and the family's structuresrc16, src17L(E^(q),1) ≠ 0 on the two smallest members, Ш(E^(313)) = 7²; one of 𝒫's conditions is implied by the others
016Tate's algorithmsrc18, src1940,749 conductors recomputed, 0 disagreements; c₂ = 1 closes the carve-out; the base has no additive prime in it
017this arm's own analytic machinerysrc20a real period wrong for three rounds, found by the rank-0 BSD identity; 285 curves close on #Ш = 1; Reg(389.a1) = 0.152460306865 — corrected to 0.15246013936831948 by 026
018the two-witness criterionsrc21[K_E:Q] = 16, e_E = 2, δ = 1/24 by exact F₂ rank — and RUN-015's redundancy is the factor e_E
019the witness-network generalisation, and §6's stop rule turned on this armsrc2231 reaches 138 of 4,063 small models that 30 cannot, all of them failing (T5); 13 meet the whole certificate; LOO fails at 2,457 primes; RUN-017's #Ш = 1 headline audited as not progress
020P5's explicit local-unit cancellation at 389.a1, p = 11src23every boxed statement of v0.8 reproduced, including v₁₁(t(16P′)) = 1 on a 38-digit point — and R ↦ [t(16R)/11] is a homomorphism with an index-11 kernel, so §6's valuation clause is basis-dependent while its rationality equivalence is not
021the P5 chain's status ledger, reconciled across ten documentssrc2444 rows, 39 gates, 5 with two statuses and all five explained; the blocking graph is acyclic; P5-LAT11 BLOCKED BY … GPR11 is ambiguous between three declared gates; and P5-BOC-NZ11 and P5-RESIDUAL-IRR11 are closed here by this tree's own computation rather than by the ledgers' citation
022P5's norm-Selmer core vertexsrc25the cube reproduced exactly — and §3's Sel = 0, §5's transversality and v1.3's det(𝓑_N) ≠ 0 are one determinant three times; {397, 991} is not special, 230 of 253 admissible pairs give a core vertex
023the rank-2 BSD identity at 389.a1src26L′′/2! = Ω·Reg closes at ratio 1.0 with this arm's own period — the first external test of RUN-017's Δ > 0 repair; the period confirmed again by integrating both real components, which agree to 5.8e−12
024the last four undrilled gates, src00–src03src11, src02every gate is now drilled; drilling them found src02's salvage detector was structurally incapable of firing — a same-line window that could never reach a verdict four lines away, and a vocabulary that read 未滿足 as 滿足; now 6 stated unmet, 0 claimed met, 0 unread
025the Phase 1 agent experiment against its own §6/§7 conditionssrc27the freeze condition 「將 analytic Ш 當 actual Ш」 is not triggered — 36 numeric Ш claims, all labelled, 5 of them in the notation itself; and the scanner needed three corrections before it measured anything
026the rank-1 BSD identity, and this tree's height extrapolationsrc28, src20the identity closes at 37a1 and 43a1 with every term computed here, ratios 1.0000000017 and 1.0000000009; and canonical_height was returning the worst of its three extrapolation levels, which corrects RUN-017's regulator precision by two orders of magnitude
027this line's own progress, measuredsrc29of the 85 documents 21 are the subject of a round, 8 are cited, 56 are not mentioned anywhere; Phase 1 has 0 subjects although six rounds verified its arithmetic — they named the artefacts, never the documents
028Phase 1's stated arithmetic against this tree's ownsrc3015 of 23 stated integers appear in our gate logs; §Q9's accounting identity checks out and four of its six inputs are ours, the two that are not being tied so one measurement closes both; and the round's own scanner failed in both directions
029§Q9's twist accounting, measuredsrc31all eight terms measured from the artefacts, so the identity is a check and not a definition of its last two; the 1,355 RUN-028 could not place is 40,749 − 39,394; and a check of mine went red on success, having frozen a finding as an invariant
030the machine-checkable arithmetic certificate for 696.e1src3228_Submission_Gate's fourth box delivered — 20 quantities each recomputed from the a-invariants alone; the first draft quoted its author and three of three were wrong; and the drill's state guard caught a memo that outlived the defect it was computed under
031Mazur's twelve isogeny degrees, for 696.e1 and every twist of itsrc33all twelve settled — eleven refuted by an explicit witness prime, and n = 2, where the sieve is structurally vacuous, settled by X₀(2); the refutation transfers to the whole family, identical on 27 of 27 good primes across three twists with 14–16 sign flips in a_ℓ; and a drill control's stated reason turned out false at n = 2
032Referee A's checklist, run as a programsrc34PASS over the four of seven base lines that are arithmetic, the other three reported as cited rather than scored; all 19 support-set members pass all five q conditions; and 200 primes the membership test rejects were put through the checklist — 0 pass, so the checklist and 𝒫 agree about who is in the family
033the GCD witness lemmas under both prime routerssrc35all three run with computed inputs — 3 split, 29 nonsplit, n_ℓ = 1 each, every gcd 1; the nonsplit restriction leaves one witness and no spare; and a searched-for curve where lemma 1 passes while lemma 3's gcd is 0, because the gcd of an empty set is 0 and every prime divides 0
03405's one exact no-go, and where it can firesrc36the no-go never fires in this family, and 𝒫's own gcd(q, 696) = 1 is why — firing at d needs the base multiplicative at d, measured to be exactly {3, 29}; and p = 3's character argument is measured special to 3 among odd primes
035the quadratic-twist invariance bridge, lemma by lemmasrc37lemma C measured on both sides — preserved at every split conductor prime on 19 of 19 members, and the split flag flips at an inert one; ℓ = 2 reported untestable after 139 inert d, not passing; and RUN-033's lone FW-H3 witness is kept alive by exactly 𝒫's split condition, since d = 17 would turn 29 split. Lemma B is where the document leaves it, so the bridge is not established
03624_Manin_Period_Audit's asserted "mod-ℓ images maximal for all ℓ"src38surjectivity certified at ℓ = 2 and every prime 5 ≤ ℓ ≤ 167 — 38 in all, six maximal classes refuted each by a named Frobenius; 11 of Mazur's twelve rise from irreducible to surjective; and ℓ = 3 is blocked by two structural facts, PGL₂(F₃) ≅ S₄ and a nonsplit-Cartan test that is vacuous mod 3
03709_FW_H3_Exact_Compiler's boxed uniform certificatesrc39the premise holds — W₋ = {29}, g₋ = 1 = 2⁰ — and the boxed ∀p>2, FW-H3 = PASS is false at p = 29: the gcd argument never sees the ℓ ≠ p clause, which empties a singleton W₋. The family theorem survives, and that is computed too — 29 is routed to P3, whose witness ℓ = 3 is split and so was never available to FW-H3
03810's ordinary obstruction and the branch FW is leftsrc40the exact criterion a_p² ≡ 1 (mod p) run over 780 good primes: 8 ordinary primes fail H2, every one with a_p = ±1, spread across the range — so no finite exception list can cover them, which is the document's own reason for the routing; the FW branch is 6 supersingular primes, H3 cleared at each, and RUN-037's exception provably cannot reach them
03911's derived supersingular FW bridge, assembledsrc41all three residual hypotheses at 6 good supersingular primes — H3 computed with witness ℓ = 29, H1 and H2 kept marked cited; L(E,1) = 1.6317… recomputed; and 11's uniform form is shown true where RUN-037 found 09's false — the same gcd, one quantifier apart, since W₋ is made of bad primes and this range is good ones. c_E = 1 stays OPEN, named in the log
04001's odd-additive period barriersrc42empty for the base (its only additive prime is 2); each member meets it at exactly q, where the twist forces (v(c₄), v(c₆), v(Δ)) = (2,3,6) — Kodaira I₀*, never II/III/IV — so 01's condition holds 19 of 19; the excluded types are constructed and the condition fails at each; p ∤ c is the weaker piece RUN-039's c_E = 1 was avoiding
041Phase 2's mother problem, with all three sets computedsrc43P_red = ∅ universally (Mazur + RUN-031 + RUN-036), P_ram = ∅ by the document's formula, P_loc not empty and not stopped — so 04's criterion is not achieved for all odd p, blocked by P_loc; the family theorem does not need it, the blocking primes being ordinary and computed disjoint from the FW branch; and 04's own warning that its P_ram formula is a heuristic turns out exact — it misses precisely the ℓ ≠ p clause RUN-037 found
042the corpus's own base certificate, row by rowsrc4422 rows: 17 recomputed here, all agree; 5 marked not computable rather than scored; and the 2-division cubic needed comparing by square class — 15's disc = −11136 and RUN-036's −45,613,056 differ by 64², so a value comparison would have reported a disagreement between two correct models; the document's refusal of the circular Ш inference is read from the file, not assumed
043this line's own position on 07's claim laddersrc45C1, and partial — H2 and H3 have exact executable meaning here, H1 is cited, and C2 is not reached at all: this arm checks residual hypotheses and cites the theorem that consumes them, and reporting higher would be 07's own fifth forbidden upgrade. All five forbidden-upgrade guards audited against the archived logs, not the prose; the three-round stop rule not triggered; 42 of 42 reports carry an explicit limits section
04425's density derivation, every field-theoretic stepsrc46disc(f₂) = −11136, F₀ = Q(√−174), Q(√−6) ⊂ Q(ζ₂₄) but Q(√29) not, [K:Q] = 16, S₃'s single nontrivial proper normal subgroup, [LK:Q] = 48, class size 2, δ = 1/24 — and the compatibility is shown against a transposition, where it fails and the density would be 0. Three routes to 1/24: this one, RUN-018's e_E/(3[K_E:Q]), RUN-009's measurement
04502's hypothesis compiler, Levels 1 and 2src47the Level-1 certificate emitted in the document's own keys for 45 odd primes — 34 FW_APPLICABLE, 4 FW_NOT_APPLICABLE, 7 UNKNOWN, every deviation an earlier round arriving (p = 3 H1, p = 7, 113 H2, p = 29 H2+H3); Level 2 not achieved, so the gate emits the mandated FW verified for tested primes and nothing more; and 02's third prohibition turns out contested by 08
046the H2 chain's consistency, and the corpus's own H3 disagreementsrc4803's Jordan–Hölder lemma and 08's ratio test verified the same statement over 22,140 character pairs, 0 mismatches; 10's single congruence is complete at every good ordinary p ≥ 5 and not at p = 3, because χ_cyc² is unramified exactly when p − 1 ∣ 2; and 02 forbids equating the divisibility criterion with H3 while 08 and 09 do exactly that — reported, not resolved
047the derived theorem before and after the refereesrc49three definitions of 𝒫, one set — 18/27's three conditions, this tree's test and Referee A's five all give the same 19 primes below 4,000 and 23 below 5,000; one of the document's conditions is implied by the other two (RUN-018 knew, over a range fifty times wider — what is new is that it sits in the corpus's own definition); of 18's five referee items 27 answers one, defers one, leaves three; and 27's six-branch router is a partition, with the witnesses it names computed here from the other end
04813's schema and 14's sieve, control includedsrc5014's odd local table recomputes exactly; the control is found by conductor, not quoted, and has a nonsplit prime and still fails — one reservoir, no distinct witness at p = 29, which is 14's whole point and RUN-033's lemma 2 returning nothing for the first time; 13's B1/B2 are RUN-033's lemma 1 and RUN-037's premise under other names; of its six obligations 1 cited, 3 partly, 2 open, none closed
049the corpus's own source audits, auditedsrc51two of this arm's conclusions move: 23 quotes the exact local condition RUN-046 said this arm did not hold, and its weight-2 specialisation a_ℓ = −1 checks out (a₂₉ = −1 nonsplit, a₃ = +1 split) — so the derivation 02 asked for is in the corpus, and 18's first referee item is addressed, not open. And 22 invokes maximality where Skinner C lists irreducibility — the stronger premise is the one RUN-036 could not certify at 3, and 22's case C is p = 3
05026's novelty rule and 01's route matrixsrc52NO HIT ≠ NOVELTY PROOF stands and none of its four remaining steps is work this arm can do; across 50 reports 21 novelty-term sentences, 11 refusals, 10 pinned quotations, 0 unaccounted — including this round's own five, pinned rather than exempted; 01's PRIMARY GO route is best covered and its STOP route untouched, while two rounds worked HOLD routes, named rather than defended
05100's enclosure consensus and 06's agent experimentsrc5300 §6 forbids three substitutions for the unclosed ∀p > 2, and the third is about this arm's own RUN-036 — all three guards are fields in the archived logs, so with 05's three and 07's five that is eleven prohibitions across three documents, audited in one place, all clear; 06's success gate stands at 2 of 4 with both gaps marked open by the corpus's own documents; and 06's step 4 wrote 「不得默認相同」 about H3 while 08 and 09 did exactly that
05202's next compiler targets and 06 v0.3's decision proceduresrc54v0.3 exists to close RUN-045's own UNKNOWN, so it was run per member and stops at its first branch: branch 1 never fires (every odd additive prime is potentially good), H3 passes with witness ℓ = 29 at all 19, H1 is UNKNOWN beyond RUN-036's range, and the isogeny-kernel test that would settle H2 is local data this tree does not compute — 2 of 5 decided. And 02's target 3 has an empty domain here: g_mult^odd = 1 has no odd prime divisor, which is inapplicable, not achieved
05304's local p-isogeny kernel criterionsrc55the test RUN-052 called unreachable was in the corpus, named in one earlier report, and the v0.3 procedure that needs it does not cite it. Its chain checks out with p odd load-bearing at step 2 — at p = 2 every point is its own negative and the criterion passes for free. And a consequence 04 does not state: λ·μ = ω, so both tests firing forces ω² = 1 ⟺ (p−1) ∣ 2, true at exactly {2,3} over 46 primes — at every p ≥ 5 the two tests are mutually exclusive. Not run on the family: its hypothesis is local reducibility and RUN-036's certificate is global
05405's family-theorem schema and 07's implementation specsrc5605 refuses to be a theorem claim; its two self-declared dangers are exactly where this line independently stopped (RUN-041, RUN-039) — agreement, not progress. Its hybrid routes p ∈ {3,5,7} away from FW, and this line has five independent structural reasons across four rounds for p = 3. 07 specifies the missing test: 6 of 14 keys fillable, 0 of 6 fixtures runnable, and its fourth forbidden inference global irreducible → local irreducible is the substitution RUN-053 refused before reading it. Prohibitions 11 → 15 across four documents
05501_Theorem_2_18_Condition_Map — first Phase 1 subjectsrc57the map recomputed on all 40,749 base curves and all 247,391 twist pairs: E1 all pass, E2 agrees with the census by set (2,709), E4 — stated by the map, never a census removal class — holds on every curve, 8b's three non-square conditions hold on all 3,747 CLZ20 curves with the 2-torsion point found by exact integer bisection, and D/E/F on every twist pair: zero failures — the admissibility side of Algorithm 2 rebuilt, not re-run. RUN-008's two populations are branches 8a/8b. And the 1,355 curves missing from the upstream twist blob are exactly the 1,355 isogeny curves
05602_Paper_vs_Current_Code_Auditsrc58the mechanism behind RUN-055's provenance finding, read from the archived diffs: Algorithm 1's isogeny rule went strict → relaxed → strict + a₃ across the three pinned commits, with the blob frozen at the first — and at 7286794 it is set(bad_primes) and set([3,5,7]), which Python evaluates to {3,5,7} unconditionally. The relaxed rule predicts all 1,355 isogeny curves in the OLD base escape its trigger: 1,355 of 1,355 do. 02 §6's pins: 1 present / 1 partial / 1 absent (paper version) / 2 N/A by the package's stated scope; §7's rank fields 0 of 4
05703 §1 + Lemma B, joined to 10 and to 27's routersrc59FW-H2 at the twisting prime decided without a kernel polynomial: ρ̄_{E_q,q} ≅ ρ̄_{E,q} ⊗ χ_q and Lemma B give FW-H2(E_q,q) ⟺ FW-H2(E,q), and at a good ordinary prime that is 10's congruence. All 19 members good and ordinary at q; exactly one has a_q² ≡ 1 (mod q) — q = 3529, a_q = 1, three independent counts. The provisional FW-everywhere design (18/02/06) fails H2 at member 3529's own twisting prime; 27's router sends p = q to BSTW and is untouched on its face. RUN-038's log had listed 3529 for seventeen rounds — four rounds held one ingredient each, none joined. Profile LEMMA_B_REDUCTION, not 07's FW17_EXACT
058this line's own 59 logs — the joins instrumentsrc60every prime set in every log intersected with every other: 100 sets, 325 intersections after filtering scaffolding, prime segments and containments; a join counts as made only if one report names the numbers and both rounds — 107 made, 218 not, and none of the 218 is a new finding. The 3529 join is in the table, and the drill sharpened the known-join test when a re-read satisfied it. The report describing the unmade joins is the document that makes them — 254 → 218 between two runs with nothing in the logs changed
05907, 11, 12, 14 — one commit, four anglessrc6107's predicates are the diff lines RUN-056 located; every figure in 11 recomputes exactly and its two pool percentages imply one pool (178,364); the histogram 11 called unknown is 2,707 / 1,353 / 2 — the fixture's 12:1 is 1:2 at 500K, right in direction; 12's delta and 14's Gate A are one operation, performed (OLD − (isogeny ∪ a₃) = CURRENT, 36,687); 14's six Gate B items all computed; Gate C run by nobody
06009 and 15 — Algorithm 2 OLD → CURRENTsrc6215's 2×2 recomputed to the pair (247,391 / 21,306 / 0 / 0, |T_O| = 268,697) with this tree's own transcription of the deleted predicate; §6 and §7 to the curve; why the expand branch could never fire — the deleted predicate is vacuous on the kept base, 0 of 36,687; 09's two synthetic cases run as claimed. Correction to RUN-055: the 1,355 identity is stated in 15 §8 and should have been cited
06108 and 03src6308's thirteen rows, 13 of 13 on first failure and LMFDB label against the 500K census under 08's own ordering; 26b1 is the BOTH class; the fixture's 9/2/1/1 is 1,233 / 115 / 7 / 2,707 at 500K; 03's six gates: four N/A by the package's scope, S4 audited at RUN-056, S6's seven fields 6 of 7 — no timestamp
06202_Official_Discrepancy_Corpus — the adversarial foursrc64the negative control RUN-055's 8b instrument never had: 62a1, 66b1, 105a1, 141c1 read from the pinned ecdata shard, none in the base, each with one rational 2-torsion point and f'(x₀) a perfect square — 4 of 4, as 02 says; a dead square test is caught only here. Three of four ainvs typed from memory were wrong. And the ecdata shard's pin reproduces only as CRLF — the package hashed a Windows checkout, 64,687 bytes = one per line
06316, 10, 01, 00, 00_v02 — Phase 1's closure and fixturessrc6516's eight items, 8 of 8 independently redone here; the <150 fixture recovered from the census — 25 → 12, 10/15 → 7/5, the 13 removed are 08's; 00's two hand fixtures reproduce exactly, no negative d ever admissible; and the other half of RUN-055: with 04's bound d < 1000, completeness holds on all 36,687 stable curves — 0 absent, 0 extra — Algorithm 2's admissibility side in both directions. 10's label not awarded
064the six Phase 1 protocol documents — Phase 1 at 23 of 25 subject + 2 cited (typed as 25 of 25; corrected at RUN-065)src6604's seven required outputs 0 of 7 by name, five with analogues; 04 refuses the full-reproduction claim and so does this line; 05's stop rule applied to this line's last twelve rounds — no freeze; 05's record fields 5 of 7 in RUN-061; 06's principle code version ≠ theorem semantics version with numbers; 06's six briefs — this line fulfils D, E, F, and D's six discrepancy classes come to 0
06502, 04, 08 — Phase 0's three maps; Phase 0 at 10 of 10src6702's four open rows still open, no report claims one closed; 4 of 7 strong-BSD components computed here, the regulator without saturation, Ш never; 04's 首選 route the most worked at 23 to 9, the 紅燈 route with no round and 0 of 85 claimants (RUN-003); 08's six briefs and Referee E's eight leaps all covered, 28 attributions verified by signature phrase; RUN-064's 25 of 25 was typed — the instrument says 23 + 2 cited, corrected
06603, 13 — the Algorithm 2 mirror and the non-monotone diff; Phase 1 at 25 of 25 in the instrument's sensesrc6803's point-count formula held against brute-force enumeration on 269,696 (curve, p) pairs, 0 disagreements; its cubic is this tree's monic form under X = 4x on all 40,749 curves; its inertness hypotheses hold on all 241,542 Zhai pairs (257,959 prime divisors, none even / non-coprime / bad / with a root); 13's +1899 / −53404 reproduced with git exactly; at entry level 0 twists added, 46,091 removed (21,306 stable + 24,785 with their base curves); every added line a comma drop (1,851) or a re-alignment (48), 0 new content; deletions account to the line
067P5 Anomalous_Norm_Localization_v1.1 — every exact figure of §2, §5, §7src69recomputed with the gate's own group law, nothing read from RUN-011: P' generates E(F₃₉₇) and E(F₉₉₁) (orders 374, 1045), Q' = 244 P' and 356 P', the four cofactor multiples, slopes 2 and 4 = the logarithms mod 11, det M_loc = 2, ρ surjective with image 390,830, the document's kernel basis a basis, v₁₁ = 2, J_S = 1; seven CLOSED_EXACT rows, one OPEN, and the ratio 3 asserted by no report of this line; θ̄_n left to RUN-068
068P5 RUGZPB_P2_P4_v0.2 — the P4 certificate's one computationsrc70mod-11 modular symbols for Γ₀(389) built here: rank 325, dimension 65 = 2g+1 with g = 32 from the genus formula, Hecke at 2, 3, 5 → 2, plus → 1, eigenvalues −5, −3, −6, 5 at 7, 13, 17, 19 as point-counted; over all 392,040 units δ₃₉₇·₉₉₁ = 5 ≠ 0 at λ(1,5) = 1, raw product sum 43,605,160 — the stress-test package's figures to the term, a third implementation; θ̄_n ≡ 5·X₃₉₇X₉₉₁ (mod I³) with the other five coefficients 0; rank-1 numbers at 397 and 991 both 0; the manuscript's 6 stays unreproduced, the theorem's input δ ≠ 0 verified
069P5 Determinantal_Kurihara_Semilocal_v1.3 — the 85th document; the sweep at 85 of 85src71det(B_N) = 2·XY computed in F₁₁[G]/I³ by the ring's own multiplication, (1+X)¹¹ ≡ 1 automatic; under all 100 generator changes the line and ord_I = 2 invariant, the coefficient reaching every unit; the ratio θ/det is 8 at the disclosed scale, 3 in the manuscript's, and primitive-root choice alone reaches all ten units — checked on the full sum for two other root pairs; Kim's hypotheses computed: ρ̄₁₁ surjective by witnesses at 2 and 3, E(ℚ₁₁)[11] = 0, c₃₈₉ = 1, torsion trivial, the Manin constant left external; 3 closed labels, 2 open, none closed here
070GPT-6's Attack 03 — a new author, the same rulessrc72Lemma 3.1's adjugate identity holds in the actual ring F₁₁[G]/I³ with det B = 2XY and over Z; every §5 constant recomputes (16 a unit, χ(U_m) = m/f_χ on all four character types, 388/389 ≡ 9, 9·5 ≡ 1, unit root 7); its §7 counterexample verified in Z₁₁[C₁₁] — h₀ = D₀u, every branch a unit, u not integral; the document labels its core lemma unproved and itself not a BSD proof
071GPT-6's Attack 04 — the mod-11 p-adic L-function at conductor 121src73reproduced from this tree's own modular symbols to the summand: c = (4,0,7,0,4,0,7,2,2,7,0), L̄(t) = 2t² + 2t³ + 2t⁴ + 5t⁶ + 6t⁷ + 10t⁸ + 7t⁹, all 110 summands identical, μ = 0, λ = 2; s₃₉₇ = 3, s₉₉₁ = 2, Euler leading terms 9t², 4t²; Theorem 7.1 read as the conditional derivation it says it is
072GPT-6's Attack 05 — the local logarithm of P and Qsrc74[16]P, [16]Q computed exactly and identical to the document's coordinates; s ≡ 99, 66 (mod 121), valuation 1; ℓ̄ = (4, 10), ker ℓ̄ ∋ P + 4Q; the Euler constant 11² · (unit ≡ 7); the height non-degeneracy and torsion derivations read, not computed
073GPT-6's Attack 06 — the multiplier 16 and the Mellin formulasrc75e₁₁/θ = 16 exactly in Q(α) with the stated fractions and 11-adic residues to 11⁸; both rank-one-update identities and the basis-change law on 500 instances; Sen matrix nilpotent; the Mellin formula with this tree's own a_n gives L''(E,1)/2 = 0.7593165002884 to 14 digits — the first computation of the corpus's value in this tree; 𝔰₁₁ and BD6 open, as stated
074GPT-6's Attack 07 — explicit secondary geometry on E × Esrc76F₆, F₈ as stated, the conic and model identities exact, S·F₈ + T·F₈′ ≡ 1 (mod 11), F₈ squarefree (genus 3); g = −(3u+2)²/d with its zero over (P,Q) and (−P,−Q); ∂Γ_PQ = 4·Z_PQ, the diagonal chains 2·Z_RR; P + Q = (−2,−1), P + R = (5/4,−13/8), Q + R = (1/9,−19/27); the Kato comparison not constructed, as the document says
075GPT-6's Attack 08 — norms, pushforwards and the scale ambiguitysrc77the three norms 7x², 7(x−1)², 7(x+2)² from Vieta exactly; A = x(T+Q), B = x(T−P) − 1, the sign identity and F_m(Γ) = 7((x+2)/y)⁴ with zero residual in the function field; div M = [R] − [P] − [Q] + [O] = m_*Z_PQ; the closed correction Θ_c with exponents (0,0,2) moving the 7 — "not Attack 06's 𝔰₁₁", as the document says; s11 null, BSD not proved
076GPT-6's Attack 09, rewritten from this side — the auxiliary character of an Eisenstein degeneration at 389.a1, p = 11src78written from the narration, before the package: the central value of the narrated E₂(1, χ₈) twist is zero twice over — weight 2 forces χ₈ = (8/·) even, w(E ⊗ χ₈) = (2/389) = −1 so L(E, χ₈, 1) = 0, and L(E, χ₈ψ, 1) = 0 for the order-5 ψ of conductor 11 too (to 10⁻¹⁵, and every χ₈-twisted plus symbol [a/11]_{χ₈}⁺ ≡ 0 mod 11) — the whole even first layer vanishes; the package's "5 mod 11" turned out to be the minus-line value at x⁻¹ (RUN-077), not any of this; all 54 fundamental discriminants to 100 in absolute value, prime to 11: root numbers, S_D, the level-11D Hecke identity, the MTT first-layer total = (1 − χ_D(11)/α)²S_D, forced vanishing 27/27, and L(E, χ_D, 1)·√D/Ω^± an exact integer (4, 16, 36, 0) tied to the mod-11 sums by one unit per sign (λ⁺ = 10, λ⁻ = 6); χ₅ and χ₋₃ the smallest whose central value survives, χ₆₅, χ₉₃, χ₋₄₇ with a vanishing one; Loeffler–Rivero's factor not reproduced, 𝔰₁₁ untouched
077GPT-6's Attack 09, the package — the Eisenstein leading term and λ₈(0)src79its number is L₁₁(E ⊗ χ₈, x⁻¹) — the odd branch at s = 0, not the central value — on the minus modular symbol: the package's 390-coordinate minus line, all forty path index sequences and values, the ten S_a, the ten measures, the sum 9 and λ₈(0) ≡ 5 reproduced coordinate for coordinate; the distribution relation at level 121; B_{2,χ₈} = 2, f_β and U₁₁ f_β = −11 f_β, (U−1)(U+11); ε²⁴ ≡ 1 + 110√2, log₁₁ ε ≡ 55√2 (mod 121); 𝒮₅(0) = 26, adjoint ≡ 3, A₀D_E ≡ 9; the [t²], [t³] extraction and 416 = 16·26; RUN-076's central-value reading corrected (same eigenline, T₉⁻ = −8⁹·9), the package's criterion passed by χ₈ and χ₅, failed only by 57, 97; Loeffler–Rivero cited, C, n, B₂, 𝔰₁₁ null
078GPT-6's Attack 10 — the circular-unit motive and the trace bridge (the last web package)src80in Z[ζ₈]: u₈ = 3 − 2√2 = ε⁻², u_bot = 17 − 12√2 = ε⁻⁴, norms, G(χ₈) = 2√2; L(1, χ₈) = log(1+√2)/√2 three ways; the 11-adic log of u_bot⁶ to 11¹⁰ exactly in Q(√2) — all nineteen term residues and L_bot, L_ε, L_ε/11, L₁₁(1, χ₈) ≡ 5, q_bot ≡ 9 identical, q_bot = 4L₁₁(1, χ₈), L_ε ≡ 55 (mod 121) matching Attack 09; B_{10,χ₈} = 28730410; the framed Frobenius entry −(12/11)L_bot; the trace model on 26 words / 676 pairs — (21), (22), (24), cocycles, rank ≤ 1, Q(a,a) = 15, Q(a,b) = 21, both pivots, the 8X, 9X variant — every row identical; no trace jet, n, C, B₂, 𝔰₁₁; its own shortcut rejected; BSD not proved
079the web GPT's Symbolic Round 001 — general cross-rank projective calibration (the first round of this line's third role: computation for the symbolic side)src81under B̂_i = C·A_i·j·z_i with a common C: (3.1), (3.2), (4.4) over every calibrator/target pair, (6.1), (7.1), (10.1), (11.1)–(11.3) hold on 126 exact formal-series instances over 21 rank patterns; (5.1) is (4.4) with λ_0 = Col_0, and with A_E(0) = 26λ₈(0)/D_E it is Attack 09's (19); supplements: Theorem 4.1 is t-covariant (both sides scale by u^{−d_i}), the bare ratio scales by u^{−(d_i−d_k)}; O5/O6 test only the common-C hypothesis (a partner-dependent C fails 30/30); log₁₁(12) ≡ 2580404199593 (mod 11¹²), v = 1, so j₁ has valuation −1; PC-001 not seen, the BF factorisation and the determinant lift unproved as the document says
080PC-001, the local GPT-6 line — the rank-0 calibrator 19.a1src82the level-19 Manin space over Q (dimension 3, T₂ eigenvalues 0, 0, 3), the plus and minus rational eigenlines identical to the line's, Hecke at 3, 5, 7, 11, 13 against point counts; every first-layer residue — α₀ ≡ 3, measures (10,6,3,10,3,3,10,3,6,10), L₁₁(E₀,1) ≡ 9, twisted sums (4,4,0,2,9,2,9,0,7,7), L₁₁(E₀⊗χ₈, x⁻¹) ≡ 4, smoothing 4, adjoint 7, product 1, the 121-level distribution relation; a₁₁(17.a1) = 0; supplement: L(E₀,χ_D,1)√D/Ω⁺ exact integers (1, 9, 36) with λ₀⁺ = 1 — the line's plus normalisation is the Néron one — and the odd twists' ratios (1, 4, 0) with one unit on the minus line; BF data, C, 𝔰₁₁, BSD not claimed by the line
081PC-002, the local GPT-6 line — the relative regulator germ and the Farey cupsrc83L_E, λ_E, L_0, λ_0 mod (11, t¹²¹) from the level-1331 layer with this line's own eigenlines — 2420 summand rows, 484 coefficients, identical; Q = L_Eλ_E/(L_0λ_0) = 7t² + 10t³ + 9t⁴ + … to t¹²⁰ identical, Weierstrass degree 2; width-11 agreement of the level-121 layer, 121 → 1331 refinement 220/220 (1331 → 14641 2420/2420 deep); the Farey cup on the cocycle spaces — rank 64 and 2, cusp-gauge radicals, J_E = 1, J_0 = 3 — Q_∪ = 3Q identical and four-line invariant; (4) and the Γ₀-to-adjoint identification read, as the line says 3 is not D_0/D_E
082the web GPT's Symbolic Rounds 002–004 — determinant lift, anchored jet, higher jetssrc84every boxed identity of the three documents instantiated exactly (exterior algebra on K², formal families in one and two variables, unit renormalisations, coordinate changes, companion operators) on 60 instances each — all hold; the gauge weights 2 (determinant) and 4 (self-paired regulator) independent of the jet order m; u ∧ v not unit-invariant, κ ∧ u is, as Round 003 says of Round 002; (17.1) by inverting the reparametrisation, (16.1) and (11.2) by substituting J⁻¹; the "calibrator power follows m" slip planted as a defect; the documents' unproved lists read
083the web GPT's Symbolic Rounds 005–007 — lattice torsor, descent and support, derived Euler defectsrc85every boxed statement instantiated on integer lattices, rational scalars, valuations and two-term complexes (40 instances each): sublattice and index-square laws, Z₁₁-invisibility of prime-to-11 indices, √3 ∈ Q₁₁ to 11¹² as the descent no-go, Hilbert 90 constructively, Smith-invariant lengths, the S-unit criterion and closure; Round 007's sign calibration adopted and shown to reproduce Round 005's sublattice law, and the mapping-cone formula δ(Cone f) = v(det B) − v(det A) computed from the cone's own differentials on every instance; which complex, which groups, S, d_ℓ — unproved, as the documents say
084the web GPT's Symbolic Rounds 010–012 — proof-obligation architecture, reciprocity-kernel dichotomy, adelic descentsrc86Round 010 read against itself (the chain (5.1), its two pure-T arrows are the named cuts T1/T6, the obligation matrix, the cut partition) and against this line's logs (S1–S8 green where instantiated; S9–S10 are the undelivered Rounds 008–009); (24.1) on 389.a1 with the tree's numbers, q_fin = 1; Round 011's statements on 40 exact instances including the leading-term theorem with its coefficient U(0)·E_e(ξ)·λ(τ_m(ξ)) and the directional failure on a rational root direction; Round 012's statements on explicit ideles of Q, the reconstruction threshold 11^k > 2MN exhaustively at 11³, and z(−x/y) of this line's [16]P, [16]Q recovered from their residues at k = 76, 104; one slip: Theorem 19.1's ε = −1 is not principal by its own Theorem 7.1 — the finite check must use ε = +1
085the web GPT's Symbolic Rounds 008–009 — self-dual fundamental line and regulator exponent; analytic leading-term line and order matchingsrc87every boxed statement on 40 exact instances: determinant pairings bilinear in the two volumes (so a², C⁴, and Reg once), Smith lengths, u^r, the placements q, q², 1, dual complexes and shifts, odd-shift cancellation, Pfaffians (det J = Pf², sign an orientation); series reparametrisation u^{−r}, frame and coordinate laws, r!, order additivity, ord ℒ = e + m with its leading form, annihilation giving e + m + 1; the regulator of 389.a1 from this line's own heights (Tate's series on 2P, 2Q, P ± Q, parallelogram law to 10⁻¹⁶): Reg = 0.15246017794314376, the corpus number to the last digit, so L''/2 = Ω·Reg·1 with every factor computed here; r_p = r_C = 2 from the mod-11 order, L(E,1) = 0 and w = +1 (two theorems cited)
086the web GPT's Symbolic Rounds 013–016 — descent audit, normalisation character, direct comparison, flat transport and holonomysrc88every boxed statement on 40 exact instances: tensor characters and their kernels, idelic cancellation, the §25 audit table against the text; the bookkeeping character (−r, 0, 1, 1, 2, 1, 1, −1) recovered from a scalar pipeline that performs each transformation, primitivity, Bezout sections, G1–G5, gauge fixing, the unit character, Smith forms; line-map torsors, cocycles, naturality forcing one ratio per component; on random graphs — holonomy gauge invariance, Theorem 6.1 both ways, one-anchor globalisation, the spanning-tree gauge, β₁ checks, gauge classes, h = −1 valuation-flat but not flat, observable holonomy, cotree defects, fault localisation; no false formula; the actual scalars, flatness and the direct theorem — unproved, as the documents say
087the web GPT's Symbolic Rounds 017–020 — flatness from naturality (H¹/H²), the normalisation fibration, universal line vs partner factors, the one-calibrator character criterionsrc89every boxed statement on 40 exact instances: natural comparisons on random graphs (coboundary transport, trivial relative holonomy with nontrivial absolute monodromy, anchor extension path-independent iff flat, projective defects as cocycles), a genuine H² obstruction over Q from carry cocycles of Z/n; no natural det H₀ → det H₂, weight bookkeeping and calibration by contraction, the reframe audit; the factor table against the text, E/L universality, the maximal calibratable lattice as an integer kernel of ratio valuations, the three mutation drills; the exact and valuation one-calibrator criteria with explicit witnesses, Smith normal forms with transforms deciding T ⊆ L_W and T ⊆ Sat(L_W); no false formula; the actual functors, factors and weight vectors — unproved, as the documents say
088the web GPT's Symbolic Rounds 021–025 — PC-001's character lattice, late vs pre-leading routes, the second anchor, non-circularity, the source search, the auxiliary leading tensorsrc90every boxed statement on 40 exact instances; PC-001's formula B̂_i = C_πA_ij z_i built as actual series with (c_lead, q_f) live, so the weights (1,−1), (0,0), (2,−2), (4,−4), (1,0) of the §20 table are measured by reframing, not read; Smith forms diag(1,0), diag(1,1); the kernel criterion a + b, the inversions; the circular anchor n_π ⊗ n_Q passes the mutation test and is rejected only by the dependency graph; the new-source theorem; the candidate table; c_m(dX)^{⊗m} coordinate-invariant, δ neutral, relative vs absolute; supplied λ₀(0)/λ_E(0) ≡ 3 (mod 11) from RUN-077/080/081, D_E/D₀ not computed; partner-independence of C_π untestable here — as the documents say
089the web GPT's Symbolic Rounds 026–030 — the defect line, period–de Rham cancellation, the K1 residual, the residual torsor, the closure theorem and DAGsrc91every boxed statement on 40 exact instances: defect ledgers, hidden characters by frame mutation, Smith valuations; the dual-frame law and the pairing product "invariant but not 1"; the K1 residual det(h⁰)/det(h¹) = det(H⁰h)/det(H¹h) on explicit complexes in random bases, trivial-cohomology automorphisms, chain homotopy, orientation parity, symplectic constraints; flat residual line systems and their sections on random graphs; the post-normalisation DAG parsed from the document — seven nodes A–G, seven obligations, a ten-item certificate, six reopening rules, twelve not-proved items ending in BSD; no false formula; C1–C10 untested for the actual PC-001, as the round says
090the web GPT's handoff after Round 035, answered — Round 030's certificate C1–C10 actualised against the actual PC-001 objects; the package handoff/PC001_NORMALIZATION_ACTUAL_AUDIT/src92one rule for every verdict, never UNMEASURED→PASS, no majority vote; C3 PASS — one cyclotomic coordinate for both partners, the γ = 12 ↔ 23 change a composition exact to t¹²⁰, jet weight u^{−r} and nothing else, PC-001's (2) covariant with log₁₁(12) cancelling; C1, C2, C4–C10 UNMEASURED, first blocker C1, NORMALIZATION-UNMEASURED, no FAIL — the objects (B̂_E, B̂_0, Π_i, Θ_aux, δ, η_pdR, the comparison map, the residual graph, the anchor) built by nobody; the measurable halves recomputed: the partner ratio's measured part 6 (mod 11), not 3, the rest one number Π_E/Π_0; the Kummer class q-blind; the calibrator's lattice data; eleven checks, fourteen planted defects; Rounds 031–035 held byte-exact, unverified
091Attack C1 — the actual-object construction, and Attack Bsrc93the auxiliary side of B̂_i built: the Eisenstein family E_k(1,χ₈) in the weight direction, a_n(X) = Σχ₈(d)d⟨d⟩^X; its pseudocharacter 𝒯_X(Frob_ℓ) = 1 + χ₈(ℓ)ℓ^{1+X} as the sum of the two Jordan–Hölder characters; the trace jet 𝒯_X(g) mod X² at eight Frobenius elements mod 11³, constant term = the actual q-expansion of E₂(1,χ₈); the characters distinct (Frob_3: 1 vs 8) ⇒ the one-dimensional Eisenstein quotient is canonical, discharging PC-001 §4's hazard; at ℓ = 11 the characters are the two roots of U² + 10U − 11, so the critical slope-1 refinement is the χ₈χ_cyc branch; Attack B computed: the generalised mod-11 eigenspace at 389 has dim 2 = the ± pair of f, and dim S₂(Γ₀(19)) = 1, so both congruence numbers are 11-units ⇒ Π_E/Π_0 is a unit and A_0(0)/A_E(0) ≡ 6·(unit) is nonzero — C1 UNMEASURED — the partner side (R_i(X,t) / the BF classes) is the one object still missing; no residue claimed for Π_E/Π_0; package handoff/ATTACK-C1-ACTUAL-OBJECT/
092Attack C4 — the arrow ε = 1+√2 ⟶ Θ_auxsrc94the target is a LINE: χ₈ is the Kronecker character (2/·) of Q(√2) (checked at 12 arguments), unit rank 1, ε⁻¹ = √2−1 so σ(ε) = −ε⁻¹ ⇒ the χ₈-eigenspace of the units is one-dimensional (derived, not asserted) ⇒ by Soulé/Bloch–Kato H¹_f(Q, Q₁₁(χ₈)(1)) is a line spanned by κ(ε); 11 inert, log₁₁(ε)/(11√2) ≡ 5 nonzero — so any nonzero Θ_aux in that group is forced to be a scalar multiple of κ(ε); and the Eisenstein weight jet is not in it: its X-direction ÷ char₂ is log₁₁(ℓ) for χ₈ and χ₅ alike at every prime ⇒ the cyclotomic class, blind to the field, living in Hom(G_Q, Q₁₁) — the naive arrow refuted on type grounds, not numerics — C4 UNMEASURED — missing: the non-split extension class at the θ-critical Eisenstein point (level 88, slope-1 overconvergent, nebentypus χ₈) plus a Bellaïche–Dasgupta/LR-A4.5-shaped comparison; the gap is now one line and one scalar; package handoff/ATTACK-C4-THETA-AUX/
093Attack C4 step 2 — the transverse extension as a dictionary, and its Selmer line's local conditionssrc95the ordering fixed once, 0 → ψ → V_Eis → 1 → 0 with ψ = χ₈χ_cyc: the matrix law forces c(gh) = ψ(g)c(h) + c(g), so the class is the upper-right entry and lies in Ext¹(1,ψ) = H¹(Q, Q₁₁(χ₈)(1)) — the target line (the reverse ordering gives (−1), a different group); lift-change = coboundary, split ⟺ coboundary, all on explicit 2×2 matrices over Z/11⁴; the four local conditions computed and ALL VACUOUS — at 11 H¹ = H¹_f (both dim 1, χ₈ unramified there with χ₈(11) = −1), at 2 H¹ = 0, at ∞ H¹ = 0 (11 odd), away from 2·11 H¹ = 0 — so membership in H¹_f is automatic, cross-checked against the global Euler characteristic; κ(ε) ≠ 0 (fundamental unit, witness q = 23); B_{2,χ₈} = 2 ⇒ L(−1,χ₈) = −1, v₁₁ = 0 ⇒ no classical mod-11 Eisenstein congruence — C4 UNMEASURED — membership CLOSED, nonvanishing OPEN, scalar OPEN (untouched by instruction); and C1's one missing map named: the pair's Rankin–Eisenstein/BF class, upstream of Eichler–Shimura — so closing C4 does not unblock C1; package handoff/ATTACK-C4-TRANSVERSE-EXTENSION/
094the Loeffler–Rivero paper read, its hypotheses computed — C4's direction closed; C1's partner-independence identified as the source's own theoremsrc96the source everything rests on was read for the first time (extracts) and its hypotheses computed on our forms: our auxiliary form is LR's E₂(1,χ₈) with ψ = 1, τ = χ₈, r = 0, N = 8 (matched to the actual q-expansion at ten primes, with α = 1, β = −11 the slope-1 root); 11-decent by Def A1.2 (cond(ψ/τ) derived, not asserted) hence non-critical by Prop A4.6(ii); Thm A6.1's reducibility ideal = 𝔪 ⇒ §A6.2 all four representations non-split ⇒ Cor A6.3(i) V(f_β) is Thm A2.1 case (3), crystalline at p, whose class lies in H¹(Q, Q₁₁(χ₈)(1)) — RUN-092's line — so crystalline puts it in H¹_f and non-split makes it nonzero; with dim H¹_f = 1, [Θ_aux] = c_ES/Kum·κ(ε). Thm C1.9 c_f(k) lives on V₁ alone, Remark C1.11 ω_f "uniquely determined by f", Thm C1.13 (= PC-001's formula (1), matched factor for factor) takes C = c*_f(r) ⇒ C_π partner-independent. Thm C1.4 gives BF existence, its hypothesis (d,6S) = 1 being exactly PC-001's d = 5 — C4-direction CLOSED, exact scalar OPEN; C1 partner-independence CITED_THEOREM, BF existence PASS-EXISTENCE, coordinates UNMEASURED — and a correction: RUN-093's "nonvanishing UNMEASURED" was wrong; package handoff/LR-HYPOTHESES-AND-C4-DIRECTION/
095Round 030's certificate re-judged with the closures fed back in — normalization audit v2src97the upgrade rests on a defect found here in RUN-090's own method: it judged all ten items with one rule (PASS only if the object was constructed), and Round 030's ten sentences are not all of one kind. Read out of the corpus file and classified by a stated lexicon: C1 is an equality, C2/C3/C8/C9 absences, C4/C6/C7/C10 existences, and only C5 — "Every defect factor is tagged E, L, G, or P" — an enumeration that no theorem label may discharge. Three things computed that no earlier round computed: (1) the hypotheses C1.1 inherits — it sends V(f,g)* to §B3.1 and Assumption B1.1 governs "throughout part B" (noble = prime-to-p level + distinct Hecke roots), while §B2 carries the paper's only residual-irreducibility assumption and the Kato class κ(g×ψ) is the partner's — all instantiated: 11 ∤ 389, 11 ∤ 19, Hecke discriminants −28, −35 (nonzero mod 11 too), and semistability computed from the Weierstrass invariants (Δ = 389, c₄ = 112; Δ = −19, c₄ = 36928, so no additive reduction — squarefreeness of Δ is not part of semistability and is kept apart as a minimal-model guard) so Mazur forbids an 11-isogeny ⇒ residually irreducible, surjectivity still not required; (2) LR equation (8) C_d = d² − d^(j−k₁−k₂)ε_f⁻¹(d)ε_g⁻¹(d) instantiated — C_d = 25 + 5^j for both partners, so RUN-090's asserted S5_partner_independent is derived from (ε_g(d), k₂) agreeing, and 𝒮₅(0) = 26 pins j = 0; (3) C_π = c_lead/q_f traced constituent by constituent — c_lead on V₁ alone (C1.9), q_f = b_f⁺(0) a trivialisation of an f-only module (§A8.3), the partner only in η_g ⇒ no partner-dependent obstruction to a common frame, so PC-001's 「共同規範是必要假設」 is a free normalisation — but §A8.3 calls b_f⁺ non-canonical, so C_π has no value until one trivialisation is fixed and anything built from C_aux inherits that ambiguity. Also: C1.9's non-vanishing clause excepts k = r, our own point — the nonvanishing is C1.13's c*_f(r) ∈ L^× — C1, C2, C4 UNMEASURED → PASS; C3 PASS unchanged, C5–C10 UNMEASURED, no FAIL, NORMALIZATION-UNMEASURED. "The first blocker" no longer has a single-item answer — Round 030's numbering says C5, a topological pass over RUN-090's own recorded dependency graph says C8, the handoff's §11 attack order says C6 and contradicts those dependencies (C6 lists C5 as upstream, C7 lists C6). The question it stood in for is what is attackable now, computed here from those upstream lists: {C5, C8} — C5 because its only upstream C4 just closed and C6/C7/C9/C10 all sit behind it, C8 because it never had an in-certificate upstream at all and is open only because nobody has attacked it; four obligations carried outside the certificate (BF-COORD, Π_E/Π_0, c_ES/Kum, the b_f⁺ trivialisation) — nothing measured this round that was not measured before; package handoff/NORMALIZATION-AUDIT-V2/
096the frontier {C5, C8} attacked — C5's defect ledger with the b_f⁺ gauge derived; C8's target saturation at level 389src98the gauge action, derived not guessed: b_f⁺ scaled by u, Attack 09's ES frame by v, only the definitions declared (the Coleman map linear in its basis vector, b_f⁺(0) linear, L-values and Kato's class blind) — then on exact instances c_f, c_lead, q_f scale by u, so PC-001's C_π = c_lead/q_f is gauge-invariant and B̂_i with it; Round 030 (15.2) δ = q_f C_π/c_aux is invariant with c_aux in the b_f⁺ frame but carries u/v with it in Attack 09's ES frame, where its C lives — a real G-factor G_b, filed in a_D; RUN-090's E tags for c_lead, q_f corrected to G. The inventory: 23 records, tags derived from four booleans by one rule, E_i split P×L, into Round 030's own bins with δ_other^E = {C_π, id(LR~PC-001), id(Kato~modsym)}, unclassified 0, duplicates 0, c_ES/Kum outside 𝒟; completeness holds relative to Round 030's architecture and stops at the comparison route, which does not exist as a map ⇒ (18.1)/(18.2) undecidable. C8 computed: src82's Manin engine at N = 389 (dim 65 = 2g+1, four Hecke primes isolate the ± pair), both Z-primitive vectors content 1, first nonzero at index 5 / 3 — where src70 / src79 normalise — with value 2 there on both signs; normalised mod 11 they equal src70's and src79's independent lines at all 390 coordinates; 11-adic saturated, not prime-to-11 saturated (index 2), globally primitive; no E-slot draws a value from any length — C5 UNMEASURED — every factor tagged, smallest missing object = the auxiliary→arithmetic comparison route (C7's object, which RUN-090's graph wrongly puts downstream of C5); C8 PASS; the peer's five C5 mutations and two C8 refusals all red; package handoff/C5-DEFECT-LEDGER-AND-C8-SATURATION/
097R0 — the comparison route realized as an actual chain of line maps; C5 re-run against itsrc99the web line's new node R0 := actual auxiliary→arithmetic comparison route exists, answered by reading rather than building: C1.13's proof — equal regulator images, then "equal as cohomology classes, by Proposition C1.1" — and C1.1's proof — H¹(Q, V(g)⊗ℋ_Γ(−j)) free of rank 1 over ℋ_Γ with Kato's class as generator and the regulator injective — so the BF leading line and the Kato line are the same rank-1 module and the arrow is line-level with the lifting theorem named; id(Kato~modsym) is Kato's theorem, not bookkeeping. Typed dictionary: Round 030's 𝒞_aux (with its Sym^m(T_X) factor and q-blindness) is LR's ω_f-framed crystalline F⁺ line (C1.10: unique, X^{−n}, m = n) — and the extension class of RUN-092–094 is the transverse line of the global-reducibility sequence, the two "cutting across each other" with cokernels t^{r+1} (LR's diagram before A8.1), their transversality being non-criticality; 𝒞_arith is the L_p(g⊗ψ)-line in ℋ_Γ, realised in-tree as src83's series. Chain Ψ = Ψ₄Ψ₃Ψ₂Ψ₁⁻¹: every arrow actual, every junction typed, the partner line a separate tensor factor, the positive control ω_f accepted ⇒ R0 PASS. C5 re-run against the chain: RUN-096's 23 records assigned to arrows with exponents; partner factors, C_d and the log cancel between Ψ₁⁻¹ and Ψ₃Ψ₄; survivors exactly a_D (G: q_f, Gauss), q_D (L: three indices), η_D (E: η_pdR, κ_det, two ids) — Round 030 §16 computed ⇒ C5 PASS; q_f and G_b shown to be one factor (C1.10 leaves one free auxiliary frame) — R0 PASS, C5 PASS; C6/C7's slots now sit on an actual arrow; the stop rule's document-level proxy answered at section granularity, transparently; package handoff/R0-COMPARISON-ROUTE-REALIZATION/
098R0.5 — the localization audit; RUN-097's category correctedsrc100the web line's objection to RUN-097 — nonzero divisor ≠ unit — decided by the tree's own data: the target's L_E = 0 + 0t + 2t² + … has a double zero, so it is not a unit of Λ and Ψ₁ is injective but not surjective whatever n, Π_E are; C_d = 26 a unit mod 11; L_0, λ_E, λ_0 Λ-units by their constant terms; c_f = X^n c_f* a unit iff n = 0 (unmeasured); log^{[r+1]} a non-unit. Arrow by arrow in the four states (unit / non-zero-divisor non-unit / fractional / zero-divisor) with the ring each inverse exists over; the composite's scalar factor by factor — every L-function and C_d cancel exactly (LR Eq. 11), X^n counted once (C = c*_f(r) is c_f with its X^n removed, which is Ψ₂'s extraction; a first draft counted it twice and the gate's own check refused it) — residual log^{[r+1]}/X^n, exactly the two named extractions — verdict C: R0 lives over ℋ_Γ-lines localized at X^n and the divisor of L_p^g, integral after the two named extractions and nowhere else — RUN-097's "over ℋ_Γ-lines" corrected; C5 kept (every divisor net 0 or a named extraction; X^n is Round 030 (14.1)'s jet order, not a δ-factor; new L-factors 0); the five mutations and the positive control planted; package handoff/R05-LOCALIZATION-AUDIT/
099C6 — the period–de Rham pairing, as objectssrc101a fourth reading of Loeffler–Rivero, Part B (B2.1–B2.3) and Eq. 11: the auxiliary pairing is C1.10's unique ω_f (at each classical weight literally "pairing with ω_{f_k}"); the arithmetic pairing is the same comparison pairing stated against a chosen Q-rational γ_g^± (B2.1) whose value on γ^± is Ω^±; one construction, two motives, the tree's ω_E measured against ω_g (λ_0⁺ = 1, λ_E⁻ = 6), never set to 1. Frame laws under Ω^± ↦ w^±Ω^± derived on exact instances, not counted from weights: L_p(g×χ) ∝ (Ω^{sign})⁻¹ (B2.2), L_p(Ad g) ∝ (Ω⁺Ω⁻)⁻¹ (B2.3), L_p^g invariant (Eq. 11), η_g invariant (forced from C1.9 — the guessed u⁻¹ is not the law), κ(g×ψ) ∝ (Ω⁺)⁻¹ forced twice, independently (C1.13's canonical left side; Kato's exact reciprocity), Ψ₄'s scalar invariant — C6 PASS / canonical, η_pdR = 1 — by theorem, the weights-only argument planted and refused; the u on the Kato → modular-symbol arrow named: q = [γ_Kato : γ_tree], a lattice index, Round 030 (10.2) ⇒ magnitude, (16) ⇒ the q_D bucket (an erratum: first filed as a_D, caught by the web line), slot re-tagged E → L, v_11(q) unmeasured; C5 kept; twelve defects and two controls planted; C7 untouched; package handoff/C6-PERIOD-DE-RHAM-PAIRING/
100C7 — determinant coherence, κ_detsrc102the determinant category fixed first — rank-1 projective modules over RUN-098's R_S = ℋ_Γ[1/X^n, 1/L_E, 1/L_p(Ad g)] in degree 0, nothing more inverted, both ends in it, log^{[r+1]} and X^n named extractions never K₁ elements; every object on the chain a module, not a complex (det(L) = L, no hidden shift — read off det RΓ, H¹ carries exponent −1 on both sides); the theorem-induced routes counted: A the chain, A′ (the regulator on the leading term) the same map as Ψ₄Ψ₃ because that is how C1.13 is proved (Eq. 11 + Kato + Prop C1.1; agreement on H¹ iff Eq. 11, checked on exact instances), B (direct f-to-g) no theorem, C (modular-symbol arrow) a change of generator by q — actual independent routes = 1; six coherence questions (convention, grading, dual, localization, orientation, induced maps) each answered yes with evidence; (18.2) implemented: h = id gives 1, an explicit automorphism accepted at 2/5 — C7 PASS / canonical, κ_det = 1 by Det's functoriality — never "one arrow on my drawing"; det(Ψ₁) over ℋ_Γ refused as K₁ (an injection between two lines), q kept out, a homotopic-to-identity map gets 1, the coherent case not refused for lack of a matrix; the eight mutations and two positive controls planted; C9 untouched; package handoff/C7-DETERMINANT-COHERENCE/
101C9 — the residual holonomy auditsrc103the complete transport graph first: RUN-097's five lines plus PC-001's B̂ vertex; Ψ₁..Ψ₄ actual, A′ the same map as Ψ₄Ψ₃ (RUN-100's identity), id a definition (PC-001 §1 names LR's object; (1) is C1.13 in six slots, matched RUN-094/095), Ψ₃^PC the same formula; every edge answers six questions; eight loops tagged G/L/P (b_f⁺↔ω_f, X, Kummer/ES, Ω^±, Gauss; q, indices; partner factors); E-labels η_pdR = κ_det = id = 1, C_π an edge label; R0.5's divisors attached to edges, never cycle labels. Quotiented in two representations: a tree (β₁ = 0) and β₁ = 7 − 6 + 1 = 2 with cycles Ψ₄⁺·A′⁻·Ψ₃⁺, Ψ₃^PC⁺·Ψ₃⁻·id⁺ both product 1 on 25 exact instances, inverses on reversed edges; a generic spanning-forest holonomy routine that accepts a tree, accepts a product-1 cycle and rejects the same cycle at 6/5; completeness from R0/C5/C6/C7 with every candidate dispositioned — C9 PASS — residual monodromy trivial, one component; C10 recorded and not claimed (trivial holonomy leaves the K^×-torsor of (20.2)); the ten mutations and two positive-control refusals planted, "one anchor fixes all components" on a two-component graph turning only the C10-boundary check red; package handoff/C9-RESIDUAL-HOLONOMY/
102C10 — the canonical-section audit; the certificate's last cellsrc104Track A first: fifteen choices, each with what it depends on, its tag, how it was quotiented and whether it survives in Ψ_red — none does (b_f⁺ → C1.10's unique ω_f; X → the leading coefficient; Ω^± cancels along Ψ₄; q in q_D; indices, partner arithmetic, C_d, the L_p factors, η_pdR = κ_det = id = 1, C_π net 0, the named extractions, n); each arrow's canonicity layer named (ω_f unique; A6.1's exponent; C1.13 lifted by Prop C1.1; Kato exact for one Betti class), none merely up to a unit; naturality across 389.a1 and 19.a1 by the same theorems with hypotheses instantiated; C9 used — a section transports path-independently along the chain, A′ and the dictionary detour on exact instances — C10 PASS / canonical, T0, s_can = [Ψ_red], ρ = 1; "ω_f alone" and "trivial monodromy ⇒ section" refused; Track B not taken but its rules enforced (four inadmissible anchor sources caught when admitted; an anchored T1 control accepted at ρ = 3, a flat unanchored system refused); external obligations kept out; PC-001 normalization certificate C1–C10 CLOSED as architecture — BSD OPEN, next Round 030's DAG A–G; package handoff/C10-CANONICAL-SECTION/
103DAG-A through the determinantal Bockstein; P5-CANON-BocID answeredsrc105four papers read and recorded verbatim (BKS 1910.07404, Kim 2203.12159, Castella–Sano 2601.14504, Macias Castillo–Sano 2603.23978); P5 v1.3's B_N typed — the canonical localization map Sel_11 → ⊕ E(F_ℓ)⊗F₁₁ dressed with chosen augmentation generators, hand-built, not the boundary of any triangle; its coefficient 2 runs over all of F₁₁^× under generator changes while the line never moves, so the candidate is [det loc_n] ∈ P(det); BKS's Boc_F is a different object (Z₁₁, degree r−1, H¹⊗H²_tf, a derived connecting morphism) and BKS Theorem 1.3's hypothesis (d) fails at exactly the Kurihara primes (E(Q_ℓ)[11] = Z/11); Kim's semi-local theorem and Theorem 3.11, hypotheses instantiated from the tree's logs, tie Kato's Kolyvagin derivative κ_{397·991}^Kato to det loc_n by an equivalence of nonvanishing and an up-to-unit scalar — lines mod 11, not elements — A PARTIAL — B_N ≠ Boc_BKS (P5-CANON-BocID closes negatively as posed); a mod-11 rank-2 derived source exists by theorem; independence from the determinant, never the rank; characteristic zero UNMEASURED (the localization target is torsion; the Z₁₁ Kolyvagin system rests on cited IMC₁₁; the canonical element is the Generalized Perrin-Riou Conjecture); smallest missing theorem named; eleven defects, three controls; B–G untouched; package handoff/DAG-A-BOCKSTEIN-IDENTIFICATION/
104DAG-A in characteristic zero: the determinantal Kato sourcesrc106Castella–Sano §1.1.4, §2.2–2.3 and Macias Castillo–Sano §2–3 read and recorded verbatim; Conjecture 2.2.2's eight objects instantiated (a₃₈₉ = +1 recomputed, so 𝒫₃₈₉ = 1 − 389⁻¹γ₃₈₉, a unit at the trivial character); ideal level / line level / distinguished element kept apart (Prop 2.2.3); the main conjecture at (389.a1, 11) PASS/CITED_THEOREM (Wan15 + BCS25 via CS Theorem B; p > 3, (sur), good ordinary, (tor_Q) instantiated); at the trivial character every local H² vanishes so H² ≅ Sel_str^∨, 16P, 16Q ∈ E₁∖E₂ give index 11⁰ and the strict line F₁₁(P + 4Q), ranks (2, 1) under the inherited Ш[11] = 0; the core rank of the relaxed structure is 1 by Prop 2.4(ii) and by (2.2.2) at the tree's vertex 397·991 (dim H¹_{𝓕^n} = 3), the ordinary one 0; Hyp 2.11 (i)–(iv) verified, RΓ_{/ur}(Q₃₈₉,T) acyclic, Theorem 3.4 applied with ring / complex / structure / lattice / degree / dual / hypotheses itemised — A PASS by cited theorem — 𝔷_{Q∞} exists, unique, a basis; 𝔷_{Q∞}(1) a basis of Z₁₁(P∧Q) ⊗ Sel_str(T) (no descent to H¹: (str-fin) fails); ε₁ a basis of SS₁(E[11], 𝓕_can) = ∧³H¹_{𝓕^n} ⊗ W₃₉₇ ⊗ W₉₉₁; core rank 1, nothing forced; A-mod11-compat UNMEASURED and not necessary (det loc_n ≠ 0 is the core-vertex certificate); the scalar ε UNMEASURED; twenty-one defects, five controls; B–G untouched; package handoff/DAG-A-CHAR0-DETERMINANTAL-KATO/
105DAG-B: the arithmetic fundamental linesrc107Rounds 032–034 read and instantiated; the actual complex fixed (CS's RΓ(Z_S,T), MCS's relaxed complex, the Poitou–Tate model: one object; the ordinary complex the self-dual hub, Nekovář shift 3); the triangle RΓ̃_ord → RΓ(Z_S,T) → RΓ(Q₁₁,T⁻) ⊕ RΓ_{/ur}(Q₃₈₉,T) as a rank ledger (2, 2, 1, 2, 1 over Z₁₁ and mod 11, alternating sums 0); the Kummer map an isomorphism in degree 1 but not a quasi-isomorphism of complexes (H²⊗Q ≠ 0), so Round 032's concentration fails and H² is kept; H² pinned by Lemma 2.14(ii) (Sel_str^∨, rank 1, torsion 11⁰); 𝒜(RΓ̃_ord) = D_MW^{⊗2} (the duality square); 𝓗_str = det(H²)⁻¹ ≅ Sel_str(T) ≅ D_MW ⊗ H¹_f(Q₁₁,T)⁻¹, checked mod 11 (6P + 2Q on the strict line); the finite package placed under the Single-Entry Rule, every 11-length 0 (Ш numeric only); the duality shift actual (3), Round 034's centre-1 profile = the ordinary complex shifted by [1] — B PASS — det⁻¹RΓ(Z_S,T) ≅ D_MW ⊗ 𝓗_str ≅ D_MW^{⊗2} ⊗ H¹_f(Q₁₁,T)⁻¹, the rank-2 MW determinant squared over the local Bloch–Kato line; the A-element transported to ε·(P∧Q)⊗R_str, ε unmeasured; C-input the strict line, kept whole; eighteen defects, four controls; C–G untouched; package handoff/DAG-B-FUNDAMENTAL-LINE/
106DAG-C: the regulator bridge, classical versus p-adicsrc108C split in two as instructed; canonical heights recomputed at depth 10 and the pairing taken by two routes (agreeing to 2.8e-9), the ½ convention discriminated by the BSD identity (0.99999975 against 0.9326/1.0168); the global index proved twice — Hermite's cap 0.2254, one cited height-difference bound (measured against 120 points), an exhaustive box of 27 points whose smallest canonical height is 0.3270; and, citing nothing, an ℓ-sieve killing every projective class mod ℓ for ℓ ≤ 19 with an explicit witness prime; MCS §4 read as a literal type (values in Q^k = I^k/I^{k+1}, 1 ≤ k ≤ 10, BD = −Nek, Hypothesis 4.1 instantiated); the formal-group ω and log computed from the minimal model — DAG-C PASS, controlled by C_NT — m = 1, so D_MW = Z(P∧Q) is primitive and det(h♭) = Reg_NT = 0.152460139; C_p PARTIAL (identification cited, nondegeneracy UNMEASURED: at k = 1 it is Schneider's conjecture); the local Bloch–Kato line is not integrally trivial — log_ω(H¹_f(Q₁₁,T)) = 11·Z₁₁, index 11, which is exactly what the refused η_pdR = 1 ⇒ local log = 1 inference would have cost; ε untouched; twenty defects, five controls; D–G untouched; package handoff/DAG-C-REGULATOR-BRIDGE/
107DAG-D: explicit reciprocity and nonannihilationsrc109D only, as instructed — the route taken arrow by arrow out of RUN-097's realised chain and RUN-098's localisation audit rather than rebuilt (Ψ₂ = C1.6 + C1.7, which is what defines D's domain; Ψ₃ = C1.13, proved scalar-first and lifted to classes by Prop C1.1; Ψ₄ = Kato's reciprocity itself); the theorem inventory read literally, including the caveat that C1.9's non-vanishing clause excepts k = r, our point, so the nonvanishing comes from C1.13's c*_f(r) ∈ L^×; D's domain written as Q = H/L with the two quotients the right way round — the τ-quotient is where C1.6 kills the class, the ψ⁻¹-quotient is where the leading term survives; exact F₁₁[[t]] arithmetic on the tree's four series — DAG-D PASS — all three layers land: D-NV1 (the class) and D-NV2 (the map) cited, and D-NV2 is stronger than asked, Prop C1.1 giving injectivity (its statement kills the kernel of loc_p, its proof supplies the regulator's nonvanishing — two different halves, both needed); D-NV3 computed here, μ(L_E) = 0 so L_E ≠ 0 in Λ while L_E ≡ 0 mod (11,t) so L_E ∉ Λ^×, with the split L̄_E = t²ū, ū⁻¹ actually computed, and ord(L̄_E·ḡ) = 2 + ord(ḡ) on 40 witnesses so nothing is annihilated. D-rational = ISOMORPHISM (a nonzero map of one-dimensional Q₁₁-spaces), D-integral = INDEX 11 (log_ω(H¹_f(Q₁₁,T)) = 11·Z₁₁), compatible, and D passes with the integral index ≠ 1; the factor entered once with its owner named, E may read it and not re-enter it. Schneider dependency NONE — no arrow of D's route is a height pairing. One finding against us: mod-11 data determines λ = 2 and μ = 0 and not the exact order of vanishing at t = 0 over Z₁₁, so the gate refuses to state the order and hands E an explicit UNMEASURED. Twenty-five defects, five controls; ε untouched; E–G not judged; package handoff/DAG-D-RECIPROCITY/
108four corrections from reviewsrc38, src71, src14, src87, src86, census_pkg懸衡's review of this line's crystallization papers, each finding re-derived before the code changed — the projective order was read off a²/q with order 10's condition in order 5's place, in two gates and in the drill check that re-verified them — at 696.e1 the A₅ witness at ℓ = 29 (q = 5, true order 5) certified nothing, now q = 11, and the 38 certified primes stand; at 389.a1 the order at q = 3 is 5, not 6, certificate unchanged; orders now computed two ways that must agree. The float64 invisibility index is where a term falls below half the running sum's last place: 208064 at s = 3, not 195684, confirmed by summing in float64 at s = 2, 3. A private path left as a fallback in census_pkg.py is gone. The rank-two identity now closes on gate 75's own L''/2, ratio 0.999999999999975, not the corpus's value at a printed 1. Six new plants; 692 defects, 692 caught; 179 controls
109the drill's crashes, counted apart; the calibrator by its a-invariantssrc11, src82, site/export_verification.py懸衡's review found the Collatz line's shared drill counting a crash and a time-out as named-check catches; the same question asked here — run_checks() scored a check that raised as red, so a defect that made its named check raise counted as caught by it. Now recorded apart: 692 planted, 687 caught by the named check, 5 detected only by a crash of it (two KeyErrors, a RuntimeError, a ValueError, a TypeError), 0 uncaught, 179 controls undisturbed. src82's log names 19.a1 by its a-invariants [0, 1, 1, −769, −8470] (Cremona's 19a2, not 19a1 = X₀(19)). The exporter states the split under the drill figures (見證's change, with this line's field added)
110no machine-local location and no account name written in the treesrc04, build_results.py, site/export_verification.py, handoff/build_handoff.pyNeo.K: every private detail goes, private trees included — src04's log names its table inside the census package, not by an absolute path (re-run, that field alone differs). The two deny-lists read the names they refuse from the machine at run time (login name, git e-mail's local part, the file AMRAL_PRIVATE_TERMS_FILE names; without it they refuse to run) instead of writing them in the code; results rebuilt 687/692 and both lines exported under them, nothing refused. build_handoff.py reads the census through BSD_CENSUS_PKG. No measured value changes

證據包

每一個 package：狀態欄位、報告、可下載檔案

重跑

從樹根執行（Python 3.10+，只用標準函式庫，不連網） 
python -X utf8 code/src11_gate_drill.py          # the whole-tree mutation drill
python -X utf8 code/src<NN>_<gate>.py          # any one gate; each round's report names its gate