Pith Number

pith:TU2QE7JX

pith:1999:TU2QE7JXXRO72V7BXARMJ4AOXB

not attested not anchored not stored refs pending

The Scaling Window of the 2-SAT Transition

B\'ela Bollob\'as, Christian Borgs, David B. Wilson, Jennifer T. Chayes, Jeong Han Kim

arxiv:math/9909031 v4 · 1999-09-05 · math.CO · math-ph · math.MP · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TU2QE7JXXRO72V7BXARMJ4AOXB}

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	2026-05-18T03:53:18.005120Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9d35027d37bc5dfd57e1b822c4f00eb8796ab5b117f8bbf20a62818fc6a6de8f

Aliases

arxiv: math/9909031 · arxiv_version: math/9909031v4 · doi: 10.48550/arxiv.math/9909031 · pith_short_12: TU2QE7JXXRO7 · pith_short_16: TU2QE7JXXRO72V7B · pith_short_8: TU2QE7JX

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/TU2QE7JXXRO72V7BXARMJ4AOXB \
  | 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: 9d35027d37bc5dfd57e1b822c4f00eb8796ab5b117f8bbf20a62818fc6a6de8f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c8d285bbb8d9d8190f0ddc5a2298453bcb76fb1a961025a4227849ebd73de0f5",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.PR"
    ],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "1999-09-05T17:26:16Z",
    "title_canon_sha256": "f39db3b569decca44ba901b9d07a4c61422919b31057babe8ccea94be8795e7b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9909031",
    "kind": "arxiv",
    "version": 4
  }
}