Pith Number

pith:RXNYAVUY

pith:2026:RXNYAVUYBP45MV4QCSG4J2JNBQ

not attested not anchored not stored refs pending

Pro-Tensor Network

Ansi Bai, Gen Yue, Linqian Wu, Tian Lan

Pro-tensor networks categorify tensor networks to study many-many-body theories without semisimplicity or finiteness.

arxiv:2605.06661 v2 · 2026-05-07 · cond-mat.str-el · hep-th · math-ph · math.CT · math.MP · math.QA

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\usepackage{pith}
\pithnumber{RXNYAVUYBP45MV4QCSG4J2JNBQ}

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Record completeness

1 Bitcoin timestamp

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 introduce the pro-tensor network, a categorification of the tensor network, as a fully rigorous yet graphically transparent framework for studying the collection of many many-body theories, which we dub many-many-body theory.

C2weakest assumption

That a well-defined pro-tensor network can be constructed and used for physical calculations while dispensing with the assumptions of semisimplicity, finiteness, and rigidity.

C3one line summary

Pro-tensor networks form a categorified framework for many-many-body theories that recovers the Levin-Wen model and characterizes particles as modules over promonads without requiring semisimplicity, finiteness or rigidity.

Receipt and verification

First computed	2026-05-20T01:06:09.814883Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8ddb8056980bf9d65790148dc4e92d0c1f465adbd122f2fef45e1f8964c26afb

Aliases

arxiv: 2605.06661 · arxiv_version: 2605.06661v2 · doi: 10.48550/arxiv.2605.06661 · pith_short_12: RXNYAVUYBP45 · pith_short_16: RXNYAVUYBP45MV4Q · pith_short_8: RXNYAVUY

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/RXNYAVUYBP45MV4QCSG4J2JNBQ \
  | 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: 8ddb8056980bf9d65790148dc4e92d0c1f465adbd122f2fef45e1f8964c26afb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d12b9e9a6326f54161e4843f7617348fc249405105716b78bb621b2ed1565630",
    "cross_cats_sorted": [
      "hep-th",
      "math-ph",
      "math.CT",
      "math.MP",
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.str-el",
    "submitted_at": "2026-05-07T17:58:40Z",
    "title_canon_sha256": "0a63ff6a2d9686c4b4e033f05fc7d41def669caa597781acdbe64ff79b003be7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.06661",
    "kind": "arxiv",
    "version": 2
  }
}