Pith Number

pith:4TW23STX

pith:2015:4TW23STXUA2CMH5J2WDAO5IUKO

not attested not anchored not stored refs pending

An Application of Markov Chain Analysis to Integer Complexity

Christopher E. Shriver

arxiv:1511.07842 v2 · 2015-11-24 · math.NT · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4TW23STXUA2CMH5J2WDAO5IUKO}

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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.

Cited by

1 paper in Pith

Upper and lower estimates for integer complexity

Receipt and verification

First computed	2026-05-18T00:53:02.809875Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e4edadca77a034261fa9d58607751453ac0dccdc9f9e8ee55f8b641ef985b589

Aliases

arxiv: 1511.07842 · arxiv_version: 1511.07842v2 · doi: 10.48550/arxiv.1511.07842 · pith_short_12: 4TW23STXUA2C · pith_short_16: 4TW23STXUA2CMH5J · pith_short_8: 4TW23STX

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/4TW23STXUA2CMH5J2WDAO5IUKO \
  | 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: e4edadca77a034261fa9d58607751453ac0dccdc9f9e8ee55f8b641ef985b589

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bc49b523ee295600402d11f0e8224ac06ec27b02bd7517d085ef8518bd5286f1",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-11-24T19:40:09Z",
    "title_canon_sha256": "f1e951d8291676fbc6539ea1efc929aea99fdbb674a16812f47673e5bf0f8715"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.07842",
    "kind": "arxiv",
    "version": 2
  }
}