Pith Number

pith:RMUMZSU3

pith:2026:RMUMZSU3S67L4G4JOFR3KJAW5S

not attested not anchored not stored refs pending

The Program Hypergraph: Multi-Way Relational Structure for Geometric Algebra, Spatial Compute, and Physics-Aware Compilation

Houston Haynes

The Program Hypergraph generalizes binary semantic graphs to arbitrary-arity hyperedges to natively represent geometric algebra and spatial dataflow constraints.

arxiv:2603.17627 v4 · 2026-03-18 · cs.PL · cs.AR

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\usepackage{pith}
\pithnumber{RMUMZSU3S67L4G4JOFR3KJAW5S}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We demonstrate that grade in Clifford algebra is a natural dimension axis within the existing DTS abelian group framework, that grade inference derives geometric product sparsity eliminating the primary performance objection to Clifford algebra neural networks without manual specialization, and that the k-simplex structure of mesh topology is a direct instance of the hyperedge formalism.

C2weakest assumption

That promoting binary edges to hyperedges of arbitrary arity preserves algebraic identity and enables joint derivation of geometric correctness, memory placement, numerical precision, and hardware partitioning inside the Fidelity framework without introducing new performance or correctness costs.

C3one line summary

The Program Hypergraph extends binary program semantic graphs to arbitrary-arity hyperedges to faithfully represent multi-way relations in geometric algebra and spatial architectures.

Formal links

2 machine-checked theorem links

Cited by

4 papers in Pith

Negative and Fractional Types in the Fidelity Framework

Fixed-Point Scaffolding in the Clef Programming Language

Dimensional Type Systems and Deterministic Memory Management: Design-Time Semantic Preservation in Native Compilation

Decidable By Construction: Design-Time Verification for Trustworthy AI

Receipt and verification

First computed	2026-06-19T16:09:56.851720Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8b28ccca9b97bebe1b897163b52416ec91f9df829722ae5d99d6aacee3491de7

Aliases

arxiv: 2603.17627 · arxiv_version: 2603.17627v4 · doi: 10.48550/arxiv.2603.17627 · pith_short_12: RMUMZSU3S67L · pith_short_16: RMUMZSU3S67L4G4J · pith_short_8: RMUMZSU3

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/RMUMZSU3S67L4G4JOFR3KJAW5S \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 8b28ccca9b97bebe1b897163b52416ec91f9df829722ae5d99d6aacee3491de7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9c4b116871976320cc1c94a60acbf8443636216c5500dfa7c5e08c3d70dfbd3e",
    "cross_cats_sorted": [
      "cs.AR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.PL",
    "submitted_at": "2026-03-18T11:47:15Z",
    "title_canon_sha256": "a13b366be98c2c4de085536363358fd2dd41ea99006c82dce52930a07fe7e2f7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.17627",
    "kind": "arxiv",
    "version": 4
  }
}