[Matarener]

Requested by Mark · project thread

Change and mathematical scope

Adds the research package research/p104-wire-routing-obstructions. This is a scoped negative result. No κ, paid-profile or scalar saving is claimed.

It asks whether lives can act as "wires" that carry the residual E = M - I into each partner's final frame Q_j, without the polluted dedicated helpers that swarm words use. It proves five structural facts and closes the minimal pollution-free form:

1. Sign lemma (hand proof + Lean third_root_or_sign). All common readers of a non-conflicting pair want the same ratio sign, except the reader whose root is the third root of the A2 through the pair.
2. Triangle lemma (hand proof + Lean triangle_iff). G_km G_mi G_ik = -1 iff the roots form an A2. There are 704 port triangles.
3. Cover lemma (finite check). Two 7-frames Q_j ∩ Q_a, Q_j ∩ Q_b cover the 48 ports of Q_j iff {j,a,b} is an A2 triangle, and then they split them 24 + 24.
4. Capacity (finite check). Such a 24-port frame has at most 16 ports in any 6-dim subframe.
5. Two-source lemma (hand proof). A chain {0} → G → Q with every live a wire, one wire per Q and no helpers is impossible.

Remaining obligations: none for the stated claims. The variant "wires plus one helper per partner G-frame" is left open.

Task and overlap

• Base: a5bff3bf1. Card p104-side-correction, scope refined: the card's premise was the feeding architecture, and this package closes the minimal form of it.
• Object: the 104 P104 ports as E8 root lines, pinned by SHA in SOURCES.json to research/p104-carrier-code-uniqueness/e8/ports.json.
• Nearest overlap: P104 carrier code: the length-8 decoding code is unique (E8 root code, min weight 49) #6166 (E8 description, A2 and third-root facts used there for decoding; here they are used for routing) and Add P104 designer toolkit v2: exact pricing and legality, #6030 rebuild with fold/hoist/retain, generators, sub-circuit tools (no kappa claim) #6170 (frame-rank law, open skeleton class). This package adds the routing lemmas 1, 3, 4 and 5 and closes one concrete architecture in that skeleton class.

Validation

python3 scripts/research_package.py --package research/p104-wire-routing-obstructions --check-only
python3.12 scripts/research_package.py --package research/p104-wire-routing-obstructions

• verify.py uses only the standard library and runs in about 7 s. It checks: V1 root model; V2 sign lemma on 4992 pairs (4224 third root is a port, 768 missing line); V3 19712 triples and 704 A2s; V4 2112 cover pairs equal the triangles, with max 24 shared ports; V5 max 16 ports in a 6-dim subframe over 2112 frames; V6 4224 23:1 splits.
• Failure controls: a perturbed port and a flipped Gram sign are both rejected.
• RESULT.json must equal the recomputed counts. Local run: PASS_REGISTERED_RESEARCH_PACKAGE.
• Lean (lean/, Lean v4.33.0-rc1, Mathlib 55b7917b): lake build OK. Axioms.lean prints only propext, Classical.choice, Quot.sound.
• Not done: lemmas 3 and 4 are finite checks, not formalized. Lemma 5 is a hand proof in PROOF.md.

Credit

Builds on the E8 port model and content-in-frame lemma of research/p104-carrier-code-uniqueness and on the #6170 toolkit theory. Prepared by Matarener with substantial AI assistance (Claude Code). Apache-2.0.

Open next questions

• Is "wires plus one helper per partner G-frame" cheaper than two polluted helpers per partner? The smallest useful follow-up is a constructive test on one A2 triangle with an exact replay.
• 3 does not divide 104, so at least 2 partners need another scheme. Our best triangle packing has 33 triangles; we have not proved it maximal.

🤖 Generated with Claude Code

https://claude.ai/code/session_011VhYmBDtuD9DJg3wmnRskB