Pith Number

pith:MG4I4NRO

pith:2025:MG4I4NRONP6DZTNHMU6QBVR4XE

not attested not anchored not stored refs pending

Local entropy theory, combinatorics, and local theory of Banach spaces

Hanfeng Li, Kairan Liu

arxiv:2507.03338 v1 · 2025-07-04 · math.DS · math.CO · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MG4I4NRONP6DZTNHMU6QBVR4XE}

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.

Cited by

1 paper in Pith

On the entropy of processes generated by quasifactors

Receipt and verification

First computed	2026-07-05T11:31:57.409720Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

61b88e362e6bfc3ccda7653d00d63cb90440a071a2a958c3fb8c80345117010b

Aliases

arxiv: 2507.03338 · arxiv_version: 2507.03338v1 · doi: 10.48550/arxiv.2507.03338 · pith_short_12: MG4I4NRONP6D · pith_short_16: MG4I4NRONP6DZTNH · pith_short_8: MG4I4NRO

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/MG4I4NRONP6DZTNHMU6QBVR4XE \
  | 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: 61b88e362e6bfc3ccda7653d00d63cb90440a071a2a958c3fb8c80345117010b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b3f5aa5defec3931302db28dd1139ec916d977c1998989ec46ee124d0882cb53",
    "cross_cats_sorted": [
      "math.CO",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2025-07-04T06:50:53Z",
    "title_canon_sha256": "6de5bf5feea9d10111efcd876f1d5abfe330bccd97fa380d69f7b50b3599d255"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.03338",
    "kind": "arxiv",
    "version": 1
  }
}