Pith Number

pith:XZGIMXHC

pith:2015:XZGIMXHCJFYZ574YVCQLSSPA52

not attested not anchored not stored refs pending

A Sard theorem for graph theory

Oliver Knill

arxiv:1508.05657 v1 · 2015-08-23 · cs.DM · cs.CG · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XZGIMXHCJFYZ574YVCQLSSPA52}

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	2026-05-18T01:34:51.990397Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

be4c865ce249719eff98a8a0b949e0ee8a92e70706e178cb7642bfce1a2d8548

Aliases

arxiv: 1508.05657 · arxiv_version: 1508.05657v1 · doi: 10.48550/arxiv.1508.05657 · pith_short_12: XZGIMXHCJFYZ · pith_short_16: XZGIMXHCJFYZ574Y · pith_short_8: XZGIMXHC

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/XZGIMXHCJFYZ574YVCQLSSPA52 \
  | 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: be4c865ce249719eff98a8a0b949e0ee8a92e70706e178cb7642bfce1a2d8548

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f75bd121a4883c7c402b0700f87cbf9e3ab1b4f3aab9a03cd5c568db3d76ea1a",
    "cross_cats_sorted": [
      "cs.CG",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2015-08-23T20:36:19Z",
    "title_canon_sha256": "556ac58ab46f459c0e72836ada52217643c05699ce2d91a58d2562273ea67579"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.05657",
    "kind": "arxiv",
    "version": 1
  }
}