Pith Number

pith:PDF6CZDI

pith:2012:PDF6CZDIIJRUDQ6HUGDPTNNBGT

not attested not anchored not stored refs pending

The Index Theorem for Quasi-Tori

Tsz On Mario Chan

arxiv:1211.6032 v2 · 2012-11-26 · math.AG · math.CV · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PDF6CZDIIJRUDQ6HUGDPTNNBGT}

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	2026-05-18T03:32:05.088718Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

78cbe16468426341c3c7a186f9b5a134fb1a76e669ffba0e73d5bb90a78358f7

Aliases

arxiv: 1211.6032 · arxiv_version: 1211.6032v2 · doi: 10.48550/arxiv.1211.6032 · pith_short_12: PDF6CZDIIJRU · pith_short_16: PDF6CZDIIJRUDQ6H · pith_short_8: PDF6CZDI

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/PDF6CZDIIJRUDQ6HUGDPTNNBGT \
  | 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: 78cbe16468426341c3c7a186f9b5a134fb1a76e669ffba0e73d5bb90a78358f7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "22bb77b35f0e78603e0d174cc1109da1a519b850b3b88e00e49b6fd2641d5e0e",
    "cross_cats_sorted": [
      "math.CV",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2012-11-26T17:37:45Z",
    "title_canon_sha256": "1e78cb93337fad5b04c38f9c7cca626821f0f6f1063411a106e5f061082c0980"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.6032",
    "kind": "arxiv",
    "version": 2
  }
}