Pith Number

pith:VZF6VILG

pith:2019:VZF6VILGPVHCKSXMGV2BAAQVLU

not attested not anchored not stored refs pending

A Reeb sphere theorem in graph theory

Oliver Knill

arxiv:1903.10105 v1 · 2019-03-25 · math.CO · cs.DM · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VZF6VILGPVHCKSXMGV2BAAQVLU}

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	2026-05-17T23:50:30.749081Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae4beaa1667d4e254aec35741002155d153cdcacf0728497358aba7a39428e6b

Aliases

arxiv: 1903.10105 · arxiv_version: 1903.10105v1 · doi: 10.48550/arxiv.1903.10105 · pith_short_12: VZF6VILGPVHC · pith_short_16: VZF6VILGPVHCKSXM · pith_short_8: VZF6VILG

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/VZF6VILGPVHCKSXMGV2BAAQVLU \
  | 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: ae4beaa1667d4e254aec35741002155d153cdcacf0728497358aba7a39428e6b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1bb8dc1c8c06ac9d4d3738f5f96588fc81ab68d552a6abe42ff19f60c8d920ab",
    "cross_cats_sorted": [
      "cs.DM",
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-03-25T02:31:41Z",
    "title_canon_sha256": "4ae2c5561b52382c990769b95b9d78f22facad935b5bdb4d7bbb6cae9b68ea07"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1903.10105",
    "kind": "arxiv",
    "version": 1
  }
}