Pith Number

pith:XG63V65B

pith:2013:XG63V65BZXZCXMHB2WSSJ2LWSM

not attested not anchored not stored refs pending

Modules over the Noncommutative Torus and Elliptic Curves

Davide Franco, Francesco D'Andrea, Gaetano Fiore

arxiv:1307.6802 v2 · 2013-07-25 · math.OA · math-ph · math.DG · 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{XG63V65BZXZCXMHB2WSSJ2LWSM}

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	2026-05-17T23:51:56.194696Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b9bdbafba1cdf22bb0e1d5a524e97693240d555d8222ecbe7f772c940faec89e

Aliases

arxiv: 1307.6802 · arxiv_version: 1307.6802v2 · doi: 10.48550/arxiv.1307.6802 · pith_short_12: XG63V65BZXZC · pith_short_16: XG63V65BZXZCXMHB · pith_short_8: XG63V65B

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/XG63V65BZXZCXMHB2WSSJ2LWSM \
  | 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: b9bdbafba1cdf22bb0e1d5a524e97693240d555d8222ecbe7f772c940faec89e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2ffcd8ced06d10200895b6b8b0995469e58d75536e6c66e8ee4fea05349c3ab8",
    "cross_cats_sorted": [
      "math-ph",
      "math.DG",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2013-07-25T16:05:58Z",
    "title_canon_sha256": "8544b5d6fd6797a76349ce5ea947724d40f56e0d3021f96f3604b1f9e7fc9bea"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.6802",
    "kind": "arxiv",
    "version": 2
  }
}