Pith Number

pith:YFR32NW6

pith:2026:YFR32NW6PJKCD7F75FKQR5VLCJ

not attested not anchored not stored refs pending

The Entropic Sum-Product Phenomenon

Rupert Li

arxiv:2607.29042 v1 · 2026-07-31 · cs.IT · math.CO · math.IT · 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{YFR32NW6PJKCD7F75FKQR5VLCJ}

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	2026-08-03T01:18:10.455508Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c163bd36de7a5421fcbfe95508f6ab125516a6a772e420642650d6c9f2d3e492

Aliases

arxiv: 2607.29042 · arxiv_version: 2607.29042v1 · doi: 10.48550/arxiv.2607.29042 · pith_short_12: YFR32NW6PJKC · pith_short_16: YFR32NW6PJKCD7F7 · pith_short_8: YFR32NW6

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/YFR32NW6PJKCD7F75FKQR5VLCJ \
  | 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: c163bd36de7a5421fcbfe95508f6ab125516a6a772e420642650d6c9f2d3e492

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a05b2db8681157790f948df2f5a2fb755939bb9172187477269b966591869894",
    "cross_cats_sorted": [
      "math.CO",
      "math.IT",
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2026-07-31T05:43:56Z",
    "title_canon_sha256": "bf81d01be2e0baf1490c057e969cdbbd31633fde2c42b4954ee9225ea737e2cb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.29042",
    "kind": "arxiv",
    "version": 1
  }
}