Established in scope
Centralizer of given carrier SU5 supplies direct E8 Petersen quantum response
In the question: Common clock sectors, quartic geometry and operational reconstruction
Closes algebraic origin of full Hodge/Petersen channel as mathematical inclusive response of same given E8 source. New50s are not old64s;family5 restricts to oldA3=4+1,not new physical generation count. Joint tensor chart instead of raw coordinate trace. Z5 center not automatically original C5/Galois/Coxeter/physical clock. P1 selection of exactly these50 insertions,their record,state and time iteration is not proved by bracket alone.
Read the exact result, assumptions and evidence
Result
Fixed carrier A4 inside D5 has exactly20 centralizer roots in same E8 with derived A4 Cartan matrix. Four50 sectors give (5,10),(10,5bar),(10bar,5),(5bar,10bar). Actual bracket(5,10) tensor(10,5bar)->(10bar,5) has50 rank12 Kraus B_mab=C_m tensor A_ab. One joint cocycle chart satisfies600 bracket edges plus1500 neutral A4+A4 action edges,including fixed dual Hodge signs. Gain12I50,normalized response Phi_Petersen tensor WH5,WH5=(Tr sigma I-sigma^T)/4. For all correlated inputs,reduced carrier response is Phi,without3/5 conditioning. All600 original P2 X charges satisfy qout+qenv=qin with dual target and qenv=-X_m.
Required assumptions
- Given full E8 current source with fixed carrier SU5
Actual weight-one E8 Chevalley source from tfpt_explorer.current_block_geometry._actual_current_source and v498. Given D5/A3 frame uses first5/last3 standard coordinates. Carrier SU5 inside D5 has roots e_i-e_j,i,j<5. Retain full E8 source,cocycle,compact form and group actions. Physical P1 realization of this already given current source is not assumed proved.
- Specified inclusive current response with invariant metric
For an explicitly specified irreducible insertion sector and input/output modules,let B_a be actual current brackets in Killing-orthonormal basis. If sum B_a*B_a=kI,E(rho)=sum B_a rho B_a*/k denotes mathematical inclusive response with unread insertion index. Reduced response uses tensor chart transported by group action. This defines tested reader,not asserted selection of physically executed P1 instrument or original time.
- Given five-slot exterior source with retained complement index
V=C5 with given oriented unitary slot basis and volume form,H=Lambda²V. C_m[kl,ij]=epsilon(m,i,j,k,l) are five distinct linear maps to conjugate target;their coherent sum is a different operation. Inner products and CAR grading remain explicit. No physical record,coupling or time iteration assumed from exterior algebra alone.
- Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
Original evidence
- E8-A4-PETERSEN-RESPONSE.txt lines 1–200
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/hodge_complement_20261028/E8-A4-PETERSEN-RESPONSE.txt
8311a51e2f9a0e5e9eb9307fc329cdce77e5d65a599da3fa5692b7460ec63a38
- E8-A4-PETERSEN-RESPONSE.txt lines 201–281
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/hodge_complement_20261028/E8-A4-PETERSEN-RESPONSE.txt
8311a51e2f9a0e5e9eb9307fc329cdce77e5d65a599da3fa5692b7460ec63a38
- E8-A4-PARENT-REVIEW.txt lines 1–52
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/hodge_complement_20261028/E8-A4-PARENT-REVIEW.txt
7199b91ec2f24c4d17a5519758c49e19a11a4bac7fd59b34f134a38de15eb221
- check_e8_a4_response.py lines 1–200
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/hodge_complement_20261028/check_e8_a4_response.py
9659806dfc92ec5f7d322a066d8e6f5b7b7c80e9a5cc285257d5d44bc57ea1f0
- check_e8_a4_response.py lines 201–400
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Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/hodge_complement_20261028/check_e8_a4_response.py
9659806dfc92ec5f7d322a066d8e6f5b7b7c80e9a5cc285257d5d44bc57ea1f0
- check_e8_a4_response.py lines 401–526
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Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/hodge_complement_20261028/check_e8_a4_response.py
9659806dfc92ec5f7d322a066d8e6f5b7b7c80e9a5cc285257d5d44bc57ea1f0
- e8-a4-results.json lines 1–200
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Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/hodge_complement_20261028/e8-a4-results.json
2816fbc59ad82469571831c4ae852753a4a147d07fd247d835b0b8adfb49c334
- e8-a4-results.json lines 201–400
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Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/hodge_complement_20261028/e8-a4-results.json
2816fbc59ad82469571831c4ae852753a4a147d07fd247d835b0b8adfb49c334
- e8-a4-results.json lines 401–574
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Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/hodge_complement_20261028/e8-a4-results.json
2816fbc59ad82469571831c4ae852753a4a147d07fd247d835b0b8adfb49c334
- VERIFICATION.json lines 1–14
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Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/hodge_complement_20261028/VERIFICATION.json
885cba19559e05306fe717f8f20532ac333a726c96c797f364eb5d04e67f876f
- CLAUDE-CLAIM-REVIEW.txt lines 1–62
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Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/hodge_complement_20261028/CLAUDE-CLAIM-REVIEW.txt
ca119cd65091fcc70c0842d96af09b82fa751595ffac03921aa5da8336b93cf0
finding:carrier-su5-centralizer-gives-direct-e8-petersen-response