Pith Number

pith:EKZNSG2H

pith:2003:EKZNSG2HDEEWZMCISHHD24JBMB

not attested not anchored not stored refs pending

Random MAX SAT, Random MAX CUT, and Their Phase Transitions

David Gamarnik, Don Coppersmith, Gregory B. Sorkin, Mohammad Hajiaghayi

arxiv:math/0306047 v2 · 2003-06-02 · math.CO · 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{EKZNSG2HDEEWZMCISHHD24JBMB}

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	2026-05-18T01:05:28.829050Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

22b2d91b4719096cb04891ce3d71216055899d9762c76281df3efa3a6e99338b

Aliases

arxiv: math/0306047 · arxiv_version: math/0306047v2 · doi: 10.48550/arxiv.math/0306047 · pith_short_12: EKZNSG2HDEEW · pith_short_16: EKZNSG2HDEEWZMCI · pith_short_8: EKZNSG2H

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/EKZNSG2HDEEWZMCISHHD24JBMB \
  | 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: 22b2d91b4719096cb04891ce3d71216055899d9762c76281df3efa3a6e99338b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "085415a75a19071724d33034511756af29abedace4940d1ae008f67b3b348edc",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2003-06-02T21:03:14Z",
    "title_canon_sha256": "cc5d6fcbfb488a48a6a37a9aed7cd0edad8fd9cca4e8a90f95dac16bc86a102c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0306047",
    "kind": "arxiv",
    "version": 2
  }
}