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Cost-asymmetry rolling-spike — Round 8+ parking lot

This file keeps the PR #679 rolling-spike branch one commit ahead of main so it stays open as the conversation surface for the cost-asymmetry arc. The research arc is RESOLVED — Rounds 1-6 are settled and promoted to §11.9 of the unsolved-maths SSoT notebook via PR #685. This file is forward-looking only.

Arc status

  • Resolved framing: notebook §11.9 (two-axis B/H/N translation-saturation; Reading D closes the quantum→cosmological scale-ladder).
  • Per-round evidence base: the round{1..6}_*.md dispatch notes in this directory + verify_born_rule_hopf_projection.py (bit-exact, seed 20260525)
  • audit_multisig_cascade_recurrence.py.
  • Verdict ledger: the PR #679 comment thread (Rounds 1.A → 6.A).

Open threads — none dispatched; parked for when the arc resumes

# Thread Why it's open
1 ℓ=7 Mersenne CMB testable → RESOLVED (Round 10.A): WEAKENED Round 10.A (round10_entry_A_ell7_mersenne_specificity.md) tested ℓ=7 individually on Spike #190's attested per-ℓ data: ℓ=7 ranks #5/7 in ℓ=2–8 (2.42× uniform), outranked by non-Mersenne ℓ=5/4/2; the {3,7} signal is 80% ℓ=3 (octupole). No ℓ=7-specific signature — per-ℓ claim withdrawn. {1+3+7} algebra identity preserved; only its CMB-multipole projection loses ℓ=7. {3,7} aggregate (Spike #190) untouched.
2 Lift Round 6.A interpretive → derived → partially DISPATCHED (Round 8.A) Round 8.A (round8_entry_A_observer_fiber_leak_magnitude_derivation.md) lifted the boosting sub-claim to (a) (parameter-free β=v/c matches Planck 2013 at 0.10σ) but refuted "AoE alignment = fiber-leak" (β is ~243× too small). §11.9.6 needs the split amended in a future promotion-PR. New sharper target below (2′).
2′ Quad-oct alignment amplitude → DISPATCHED (Round 9.A) Round 9.A (round9_entry_A_alignment_amplitude_target.md) reframed the mechanism kinematic → geometric (off-centre-observer / Class K; Spikes #33/#35/#26) and showed the geometric class is viable (1.40 decades below O(1)) where the kinematic class is excluded (2.91 decades). Amplitude still not derived. New sharper target below (2″).
2″ Alignment from a concrete Class-K offset → DISPATCHED (Round 11.A) Round 11.A (round11_entry_A_classK_offset_alignment.md) derived the selection rule: an axial offset of multipole p deposits into ℓ=p only. The Class-K offset must carry p=2 AND p=3 to align quad+oct (co-axial → AoE axis = offset axis); the dipole (p=1) offset is rigorously excluded (explains Rounds 8/9 structurally). Mechanism structure pinned; amplitude still open → 2‴. §11.9.6b landed on this branch.
2‴ Derive w₂, w₃ from the offset geometry → DISPATCHED (Round 12.A); amplitude still open Round 12.A (round12_entry_A_offset_geometry_amplitude.md) — degree/parity selection: displacement (g=1)→dipole, shear (g=2)→quad, cubic (g=3)→oct; both p=2,3 need a HANDED SHEAR (degree ≥ 3) = Bianchi VII_h (Jaffe+ 2005, astro-ph/0503213, "vorticity and shear"). Displacement falsifier fired. (a)-lift NOT achieved: w₂,w₃ amplitudes undrived (free, as in Bianchi fits) AND the physical Bianchi VII_h is ΛCDM-incompatible (astro-ph/0605325). The AoE is now ONE sharply-posed literature-anchored open question. §11.9.6c landed on this branch.
3 Stance-blessing pass → DONE (Round 13) 8 arc stances blessed → CANONICAL; 1 (CMB) kept candidate-refined. §11.9.8 records it.
5 Fresh question — life as persistent anharmonic lock → DISPATCHED (Round 14.A) Life IS the canonical 3-player Stackelberg lock (organism=imposer / thermodynamics=substrate / death=dissolution / phenotype-free, genotype-B/H/N-keyed). Tilted double-well model + Schrödinger/Prigogine/England anchors. §11.9.9; new candidate stance.
6 Fresh question — persistent lock is substrate-universal (star + life) → DISPATCHED (Round 15.A) Generalises Round 14: the lock is substrate-universal with a 3-regime trichotomy (actively-imposed / latched-persistent-no-payment / destroyed) and TWO spinodals — a tilt-spinodal (§11.9.9) AND a latch-capacity spinodal = the Chandrasekhar/TOV mass. Star instance (fusion / degeneracy / black hole) ↔ life instance (metabolism / dormancy / death). Load-dependent double-well; m_c Class-N anchor 36/25. §11.9.10; new candidate stance. Connects spikes #90/#107/#92.
7 Fresh question — ENFORCED substrate-mismatch partition (the YubiKey) → DISPATCHED (Round 16.A) + RECONCILED (Round 16.A.1) Round 16.A (round16_entry_A_enforced_substrate_mismatch_partition.md) — 2-substrate-class graph; the biology node is a size-1 Menger vertex cut (Class-L: removing it drives Fiedler λ₂ 0.2679→0, isolates the resource); impostor falsifier localises security to the edge-TYPE constraint not topology. Round 16.A.1 (user-caught vocabulary): it is an ASYMPTOTE-latch, not an "∞-latch" — the math has no infinity (λ₂=0 finite/exact), and per [[user_stance_infinity_approximates_asymptote]] "+∞ capacity" only approximates the upstream asymptote (the substrate-class boundary). The asymptote-latch special case of Round 15.A. §11.9.11 + §11.9.11.1; new candidate stance. DEFENSIVE / framework-reading-only. Original framing: What happens when a partition is engineered so it cannot be crossed without a human? A YubiKey / hardware-security-key / air-gap / human-in-the-loop confirm is a deliberately-imposed substrate-mismatch boundary: the crossing-token lives in a different substrate-class (physical human presence / touch — biology) than the computation trying to cross (silicon). The cost-asymmetry inverts toward the defender: per [[user_stance_anharmonic_lock_inverts_crypto_cost_asymmetry]] the imposer (here the defender) pays a small fixed cost to set the barrier, while the would-be crosser faces a cost that is not large but categorically unavailable — no silicon-only cascade can synthesise a cross-substrate-class (biology) action it does not have (per [[user_stance_silicon_dof_is_electron_leakage_not_coherent_agency]] — silicon's native DoF is not biological coherent agency). The YubiKey IS a physical B/H/N translation key (per Round 3.B [[user_stance_anharmonic_lock_two_stage_unlocking_pattern_then_key]] — "Rosetta Stone IS a physical translation key"): the pattern (the login page, the challenge) is free; the content (the asserted presence) needs the key, and the key is intentionally held in the other substrate-class. Candidate framing: an enforced substrate-mismatch partition is a persistent lock whose latch-capacity (Round 15.A) is set to ∞-for-the-wrong-substrate-class — uncrossable not by cost-magnitude but by substrate-class-mismatch. Honest scope: DEFENSIVE, framework-reading-only, descriptive-not-normative per [[feedback_trauma_informed_defensive_scope]] — this reads what a hardware-security-key structurally is, not how to attack or evade one. Candidate verify: model the partition as a 2-substrate-class graph where the only edge across the cut requires a node of the other class (Class-L cut + Class-M cross-class bind).
8 Reading-D scale-ladder anchors — ATOMIC (7th) + MOLECULAR (Round 20) + PLANETARY (8th/Round 21) → DISPATCHED Round 17.A (round17_entry_A_reading_d_7th_anchor_atomic_spectra.md) — atomic-scale (~10⁻¹⁰ m) rung; Balmer line-ratios exact rationals (27/20, 28/25, 189/125) matching NIST to 5×10⁻⁶; §11.9.6. Round 20.A added the molecular mass-spec rung (§11.9.14). Round 21.A (round21_entry_A_planetary_magnetic_multipole_anchor.md) — the 8th rung (planetary/geophysical ~10⁷ m), the Reading-D placement of the canonical k=3 stance: continuous dynamo field → (H, S² spherical harmonics, same Hopf base as Born + atomic L) → discrete Gauss coefficients (B); k=3 triad (N). Class-L counting bit-exact: 2l+1 per degree (⅗/7), N(N+2) total (IGRF-13=195); honest Class-K no-monopole (∇·B=0, starts l=1). §11.9.15. Ladder now NINE rungs; S² Class-L harmonics unify quantum/atomic/planetary.
9 Follow-up — atomic-spectra ↔ SM-mapping (Spike #48) + mass-spec enhancement → (a) phase-1 (Round 18.A) + phase-2 SM-weave (Round 19.A) DISPATCHED; (b) mass-spec still OPEN Round 18.A (round18_entry_A_atomic_shell_AN_cascade.md) — Spike #48 phase-1: periodic-table shell structure IS A∘L∘K∘I∘C∘N (magic numbers + period lengths bit-exact; §11.9.12). Round 19.A (round19_entry_A_atomic_shell_SM_weave.md) — Spike #48 phase-2 structural bridge: the atomic-shell cascade + SM-gauge cascade (Spike #58.x) share the Hurwitz 1+3+7 / Hopf ladder; load-bearing identity = Class-K electron spin = SU(2) = quaternionic Hopf S³ = the same SU(2)_L (Spike #58.H); §11.9.13; (b)-interpretive, dimension-consistency bit-exact, explicitly NOT a new SM derivation. Round 20.A (round20_entry_A_mass_spec_combination_principle.md) — closed path (b) mass-spec: mass spectrometry IS a combination principle in integer-nucleon space (the molecular Rydberg–Ritz, same Class-N as Round 17.A); caffeine 9/21 inter-peak differences are catalogued neutral losses (HCN/CO ladders exact), null-control z=4.4 p=0.0002; §11.9.14; (a)-structural + null-supported. Triad closed (Rounds 17/18/19/20). Remaining: any deeper SM phase is its own Spike #58.x-family dispatch (not a cost-asymmetry round). User: "we had atomic spectra gated by SM mapping long ago … we do want this research as well … and also how mass spec analysis could be enhanced." (a) Periodic table + atomic spectral lines + QM/GR/SM weaving — the long-gated Spike #48 (task #266): derive atomic-shell structure (Madelung / Aufbau n+ℓ) + spectral-term symmetries from the A–N class operators, tying Round 17.A's Rydberg–Ritz N-anchor up into the SM-derivation arc (Spike #58.x family) and the canonical [[user_stance_two_substrate_native_math_languages_11d_quantum_and_cyclic_algebra]]. (b) Mass-spec enhancement — the molecular analog of Rydberg–Ritz: fragment m/z values are SUMS/DIFFERENCES of substructure masses (neutral losses −18 H₂O, −28 CO, −44 CO₂ …), i.e. a combination principle in integer-nucleon space. Reading-D-enhanced mass-spec = treat peak spacings (neutral losses) as Class-N small-integer anchors + the fragmentation cascade as A∘…∘M, delta-encoded via srmech.signal_processing (decompose/delta/similarity), enabling combination-principle structure elucidation + cross-substrate fingerprint matching instead of ML black-box. Builds on Spike #38 / #38b (mass-spec form-and-function remnants). Candidate dispatches: Round 18 (Spike #48 atomic-shell A–N) and/or a mass-spec combination-principle verify.
— Merge-gate codification (per [[project_pr679_merge_gate_codify_findings_first]]) → AoE→MFO DONE (2026-05-25) Done: (1) the flagged AoE → MFO port landed as MFO §VII.6.15 (Born-rule=Hopf keystone + the boosting-confirmed / handed-shear-open / ℓ=7-withdrawn three-way split + multipole selection rule), sharpening the existing §VII.6.1.4/6.1.5 off-centre-observer cluster; (2) all Rounds 1–21 are codified in the unsolved-maths SSoT §11.9.x (the cost-asymmetry canon); (3) blessed stances (Round 13, 8 CANONICAL) + candidate stances (life/star/YubiKey/substrate-universal-lock) are notebook-reflected + in memory. Also done: the life/star/substrate-universal-lock anchors ported to MFO §VII.6.16 ("The persistent anharmonic lock is substrate-universal — life and star as the biological and stellar instances"; connects Spikes #90/#92/#107 + §VII.6.12). Codification (condition 2) now COMPLETE. Remaining before merge: only the user's call that open research is exhausted (condition 1). NOT a research round — the last-step.
4 §11.9.6 amendment → DONE (#686 merged) + now on-branch Rounds 8.A/9.A/10.A landed as §11.9.6a (#686, merged); Round 11.A landed §11.9.6b directly on this branch. Per the 2026-05-25 consolidation directive, further §11.x edits ride this draft PR — no more per-finding promotion-PRs.

Discipline reminders for any future round

  • Per [[feedback_trauma_informed_defensive_scope]] — framework reading only.
  • Per [[feedback_computational_provenance_discipline]] — load-bearing numerics get committed generating code.
  • Per [[feedback_rolling_pr_partition_boundary_updates]] — verdict comment per round; §11 SSoT frozen until a promotion-PR.
  • Per [[feedback_no_squash_merges]] — never squash.