Pith Number

pith:TOZGVGZX

pith:2012:TOZGVGZXUH4NR5WHRPFCVMJJ5O

not attested not anchored not stored refs pending

Module Structure on Invariant Jacobians

Nanhua XI

arxiv:1204.6131 v1 · 2012-04-27 · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TOZGVGZXUH4NR5WHRPFCVMJJ5O}

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	2026-05-18T03:56:46.922361Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9bb26a9b37a1f8d8f6c78bca2ab129eb90cc758d61a4180872971ff36a42db4d

Aliases

arxiv: 1204.6131 · arxiv_version: 1204.6131v1 · doi: 10.48550/arxiv.1204.6131 · pith_short_12: TOZGVGZXUH4N · pith_short_16: TOZGVGZXUH4NR5WH · pith_short_8: TOZGVGZX

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/TOZGVGZXUH4NR5WHRPFCVMJJ5O \
  | 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: 9bb26a9b37a1f8d8f6c78bca2ab129eb90cc758d61a4180872971ff36a42db4d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fab644eb26cf34add837fa4a9aa15c01179069440ae3234fb9199b1d800c8da5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2012-04-27T07:57:43Z",
    "title_canon_sha256": "115a5271309ad7ddcdd98adec599928ec998d4a53502901ccb72c02526a0c181"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.6131",
    "kind": "arxiv",
    "version": 1
  }
}