Pith Number

pith:XJ76F5ZI

pith:2015:XJ76F5ZIQYXG7TYF6OJYZGEMCO

not attested not anchored not stored refs pending

Dual of Bass numbers and dualizing modules

A.-J. Taherizadeh, M. Rahmani

arxiv:1508.05813 v3 · 2015-08-24 · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XJ76F5ZIQYXG7TYF6OJYZGEMCO}

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	2026-05-18T01:17:32.983772Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ba7fe2f728862e6fcf05f3938c988c13a63a7545856eb71d2b0f1661f6838d1d

Aliases

arxiv: 1508.05813 · arxiv_version: 1508.05813v3 · doi: 10.48550/arxiv.1508.05813 · pith_short_12: XJ76F5ZIQYXG · pith_short_16: XJ76F5ZIQYXG7TYF · pith_short_8: XJ76F5ZI

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/XJ76F5ZIQYXG7TYF6OJYZGEMCO \
  | 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: ba7fe2f728862e6fcf05f3938c988c13a63a7545856eb71d2b0f1661f6838d1d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6b91573f8f2bc8fcbffce432d444be1a510a9e259fc2ad393bcc2563e51ccb26",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2015-08-24T14:09:33Z",
    "title_canon_sha256": "ba88a006e481b71c352403e3bb6ccfdf985cc5df9dc638f1d2cc5dc5febebae7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.05813",
    "kind": "arxiv",
    "version": 3
  }
}