Pith Number

pith:7JOWN5TA

pith:2015:7JOWN5TASC3EEKWJS53USDNJ2C

not attested not anchored not stored refs pending

Non-Associative Geometry of Quantum Tori

Davide Franco, Francesco D'Andrea

arxiv:1509.05347 v3 · 2015-09-17 · math.QA · math-ph · math.MP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7JOWN5TASC3EEKWJS53USDNJ2C}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

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.

Receipt and verification

First computed	2026-05-18T01:21:11.398169Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fa5d66f66090b6422ac99777490da9d0b6cd4c4fd8572aeec82d36ce4da9d728

Aliases

arxiv: 1509.05347 · arxiv_version: 1509.05347v3 · doi: 10.48550/arxiv.1509.05347 · pith_short_12: 7JOWN5TASC3E · pith_short_16: 7JOWN5TASC3EEKWJ · pith_short_8: 7JOWN5TA

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/7JOWN5TASC3EEKWJS53USDNJ2C \
  | 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: fa5d66f66090b6422ac99777490da9d0b6cd4c4fd8572aeec82d36ce4da9d728

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "11d3dc62c9dab745f3ac715421cbacbedab19d093e052482ad2c9d6ab39d2b7a",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2015-09-17T17:54:37Z",
    "title_canon_sha256": "0d865a5025fd8a4f1adf25befd3f64df08b5d90db327fc1994e007eb5937e0ac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.05347",
    "kind": "arxiv",
    "version": 3
  }
}