Pith Number

pith:7KAFAFLA

pith:2005:7KAFAFLA6YLSZ3X4HBHSGPDWKN

not attested not anchored not stored refs pending

A definition of descendants at one point in graph calculus

Sergei Shadrin

arxiv:math/0507106 v2 · 2005-07-05 · math.QA · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7KAFAFLA6YLSZ3X4HBHSGPDWKN}

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	2026-05-18T00:10:32.592771Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fa80501560f6172ceefc384f233c76537cfcb7d719f91eaae6276ac364a92970

Aliases

arxiv: math/0507106 · arxiv_version: math/0507106v2 · doi: 10.48550/arxiv.math/0507106 · pith_short_12: 7KAFAFLA6YLS · pith_short_16: 7KAFAFLA6YLSZ3X4 · pith_short_8: 7KAFAFLA

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/7KAFAFLA6YLSZ3X4HBHSGPDWKN \
  | 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: fa80501560f6172ceefc384f233c76537cfcb7d719f91eaae6276ac364a92970

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dc7fa5af47732f292652f2b286ff077ef173c82cf2174902ad8360a63646360c",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "",
    "primary_cat": "math.QA",
    "submitted_at": "2005-07-05T20:08:35Z",
    "title_canon_sha256": "65fab4c9820e39828ec07f63025d3aae52c07695689e6212b74e427017775c5d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0507106",
    "kind": "arxiv",
    "version": 2
  }
}