Pith Number

pith:2PZP7XMN

pith:2011:2PZP7XMNO5K33T4MRXLHFBKN2P

not attested not anchored not stored refs pending

Modular Curvature for Noncommutative Two-Tori

Alain Connes, Henri Moscovici

arxiv:1110.3500 v2 · 2011-10-16 · math.QA · math.DG · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2PZP7XMNO5K33T4MRXLHFBKN2P}

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	2026-05-18T03:10:37.592632Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d3f2ffdd8d7755bdcf8c8dd672854dd3d122d9c0d5a320af9dc3cba4337189c5

Aliases

arxiv: 1110.3500 · arxiv_version: 1110.3500v2 · doi: 10.48550/arxiv.1110.3500 · pith_short_12: 2PZP7XMNO5K3 · pith_short_16: 2PZP7XMNO5K33T4M · pith_short_8: 2PZP7XMN

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/2PZP7XMNO5K33T4MRXLHFBKN2P \
  | 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: d3f2ffdd8d7755bdcf8c8dd672854dd3d122d9c0d5a320af9dc3cba4337189c5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "48f583fbce1305331f7ee2089f0b220a992904fe604ee618a7ac187e68291af9",
    "cross_cats_sorted": [
      "math.DG",
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2011-10-16T16:46:04Z",
    "title_canon_sha256": "53dd36be3b1a74e3f6d438b0c86aaad18cbb43d7a7b37db4255a982788f56bbc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.3500",
    "kind": "arxiv",
    "version": 2
  }
}