Pith Number

pith:7A7YPCFP

pith:2021:7A7YPCFP57EIKWYA5J3AVCZAZY

not attested not anchored not stored refs pending

The Curvature of Graph Products

Oliver Knill

arxiv:2107.08563 v1 · 2021-07-19 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7A7YPCFP57EIKWYA5J3AVCZAZY}

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	2026-07-05T02:58:50.362329Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f83f8788afefc8855b00ea760a8b20ce071f8d68212069c4c6640ef5028d8a00

Aliases

arxiv: 2107.08563 · arxiv_version: 2107.08563v1 · doi: 10.48550/arxiv.2107.08563 · pith_short_12: 7A7YPCFP57EI · pith_short_16: 7A7YPCFP57EIKWYA · pith_short_8: 7A7YPCFP

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/7A7YPCFP57EIKWYA5J3AVCZAZY \
  | 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: f83f8788afefc8855b00ea760a8b20ce071f8d68212069c4c6640ef5028d8a00

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f19fee2fd3d55b09549bfce63009fde2faf8386d6f9103dfe9893844e2dbce38",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2021-07-19T00:15:28Z",
    "title_canon_sha256": "8d7faee580178462736d41f3cfa9c2bea7804f5290b39f7170b87ce52cc0ceb1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2107.08563",
    "kind": "arxiv",
    "version": 1
  }
}