Pith Number

pith:Y253O7XN

pith:2011:Y253O7XN7ORAAD3MCQPUXM47CJ

not attested not anchored not stored refs pending

Distributivity versus associativity in the homology theory of algebraic structures

Jozef H. Przytycki

arxiv:1109.4850 v1 · 2011-09-22 · math.GT · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Y253O7XN7ORAAD3MCQPUXM47CJ}

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	2026-05-18T04:12:32.793055Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c6bbb77eedfba2000f6c141f4bb39f124a640ffc85b149dadebc4bedb18903f5

Aliases

arxiv: 1109.4850 · arxiv_version: 1109.4850v1 · doi: 10.48550/arxiv.1109.4850 · pith_short_12: Y253O7XN7ORA · pith_short_16: Y253O7XN7ORAAD3M · pith_short_8: Y253O7XN

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/Y253O7XN7ORAAD3MCQPUXM47CJ \
  | 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: c6bbb77eedfba2000f6c141f4bb39f124a640ffc85b149dadebc4bedb18903f5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a904fd86a30cd5170017e3f3711c1628dbf0120dbcf4a3a3e0cf1af61ead6e26",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-09-22T15:38:50Z",
    "title_canon_sha256": "d8558890d15d7c7f437c365ac42de51d1b094a36ba695f90cf0865455b9546e2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.4850",
    "kind": "arxiv",
    "version": 1
  }
}