Pith Number

pith:VADQXOBE

pith:2018:VADQXOBE2DTSKHF3Z5WOR72ASR

not attested not anchored not stored refs pending

The critical exponent: a novel graph invariant

Apoorva Khare, Bala Rajaratnam, Dominique Guillot

arxiv:1802.06976 v1 · 2018-02-20 · math.CO · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VADQXOBE2DTSKHF3Z5WOR72ASR}

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	2026-05-18T00:22:53.811596Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a8070bb824d0e7251cbbcf6ce8ff4094590b499224f6ded4d64ad4550db818c8

Aliases

arxiv: 1802.06976 · arxiv_version: 1802.06976v1 · doi: 10.48550/arxiv.1802.06976 · pith_short_12: VADQXOBE2DTS · pith_short_16: VADQXOBE2DTSKHF3 · pith_short_8: VADQXOBE

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/VADQXOBE2DTSKHF3Z5WOR72ASR \
  | 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: a8070bb824d0e7251cbbcf6ce8ff4094590b499224f6ded4d64ad4550db818c8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bd9265b8fd7cb3a9acf6bfa8e31f5fa0416c1f576bdf6d4d81ea0c04e7f4db8a",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-02-20T06:09:35Z",
    "title_canon_sha256": "f79f047919dbef66466b9ecbd25cbc6ea4d81952661e30cf8ab0b6a95012ae74"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1802.06976",
    "kind": "arxiv",
    "version": 1
  }
}