Pith Number

pith:FF7MLZI6

pith:2019:FF7MLZI6AWZWF67IXQES6G25CX

not attested not anchored not stored refs pending

Closure of VP under taking factors: a short and simple proof

Chi-Ning Chou, Mrinal Kumar, Noam Solomon

arxiv:1903.02366 v2 · 2019-03-06 · cs.CC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FF7MLZI6AWZWF67IXQES6G25CX}

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	2026-05-17T23:48:09.118349Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

297ec5e51e05b362fbe8bc092f1b5d15ed70eeb1e2efe06f368a126b0c15cd9f

Aliases

arxiv: 1903.02366 · arxiv_version: 1903.02366v2 · doi: 10.48550/arxiv.1903.02366 · pith_short_12: FF7MLZI6AWZW · pith_short_16: FF7MLZI6AWZWF67I · pith_short_8: FF7MLZI6

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/FF7MLZI6AWZWF67IXQES6G25CX \
  | 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: 297ec5e51e05b362fbe8bc092f1b5d15ed70eeb1e2efe06f368a126b0c15cd9f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "27267639f5f614fedd845f1b517bc0d212a263410f617f73cb2766594998fc73",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2019-03-06T13:31:46Z",
    "title_canon_sha256": "2ba130805513df505fffbc4bb632b5c85b283dfb0b911538c02d2c69a80e7e65"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1903.02366",
    "kind": "arxiv",
    "version": 2
  }
}