Pith Number

pith:4P4DCGZV

pith:2016:4P4DCGZVPSLXTG6HL2TDBFAVNL

not attested not anchored not stored refs pending

Phases in Large Combinatorial Systems

Charles Radin

arxiv:1601.04787 v2 · 2016-01-19 · math.CO · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4P4DCGZVPSLXTG6HL2TDBFAVNL}

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	2026-05-18T01:19:53.091795Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e3f8311b357c97799bc75ea63094156adc080c28b93fa66be87946dbec3b3cf6

Aliases

arxiv: 1601.04787 · arxiv_version: 1601.04787v2 · doi: 10.48550/arxiv.1601.04787 · pith_short_12: 4P4DCGZVPSLX · pith_short_16: 4P4DCGZVPSLXTG6H · pith_short_8: 4P4DCGZV

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/4P4DCGZVPSLXTG6HL2TDBFAVNL \
  | 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: e3f8311b357c97799bc75ea63094156adc080c28b93fa66be87946dbec3b3cf6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1133546934c8a622709129ab41a0f50b059f4ddb25845388e6c5c9fb7751ed0a",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-01-19T03:34:32Z",
    "title_canon_sha256": "4835e74f6db632b7c6c44e58f607c82382770c7fe942a71de2a2ed05c4f232aa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.04787",
    "kind": "arxiv",
    "version": 2
  }
}