Pith Number

pith:5QYLBIKQ

pith:2015:5QYLBIKQJ5BG5XMN3UPJTM7R2A

not attested not anchored not stored refs pending

On the replica symmetry phase of the independent set problem

Marius A. Schmidt, Nicola Kistler

arxiv:1512.04462 v2 · 2015-12-14 · 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{5QYLBIKQJ5BG5XMN3UPJTM7R2A}

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	2026-05-18T01:24:13.973950Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ec30b0a1504f426edd8ddd1e99b3f1d01554be4303834695d867f8343d6a7041

Aliases

arxiv: 1512.04462 · arxiv_version: 1512.04462v2 · doi: 10.48550/arxiv.1512.04462 · pith_short_12: 5QYLBIKQJ5BG · pith_short_16: 5QYLBIKQJ5BG5XMN · pith_short_8: 5QYLBIKQ

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/5QYLBIKQJ5BG5XMN3UPJTM7R2A \
  | 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: ec30b0a1504f426edd8ddd1e99b3f1d01554be4303834695d867f8343d6a7041

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4681337621524c16e53fd128764a1f7bf6cf998713d938e3ab320a9a14e2957e",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-12-14T19:05:01Z",
    "title_canon_sha256": "e4e0797f2b346a8895d94dd0c1b0d3ba31ca95250ae0c8313dc7e65cc5935bb2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.04462",
    "kind": "arxiv",
    "version": 2
  }
}