Pith Number

pith:NRCGX72O

pith:2025:NRCGX72ORBORCS4OHYX5HR7ZDW

not attested not anchored not stored refs pending

Low Sets and Closure Properties of Counting Function Classes

Yaroslav Ivanashev

arxiv:2507.04110 v4 · 2025-07-05 · cs.CC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NRCGX72ORBORCS4OHYX5HR7ZDW}

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	2026-07-28T01:22:20.991719Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6c446bff4e885d114b8e3e2fd3c7f91da558e722828e3f7dca27f2a16c19651d

Aliases

arxiv: 2507.04110 · arxiv_version: 2507.04110v4 · doi: 10.48550/arxiv.2507.04110 · pith_short_12: NRCGX72ORBOR · pith_short_16: NRCGX72ORBORCS4O · pith_short_8: NRCGX72O

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/NRCGX72ORBORCS4OHYX5HR7ZDW \
  | 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: 6c446bff4e885d114b8e3e2fd3c7f91da558e722828e3f7dca27f2a16c19651d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e2e2af3c5fd788ffe2074834fa0a53c66409a9ad5aa8207117c6191360ae9aae",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2025-07-05T17:40:08Z",
    "title_canon_sha256": "ae6ca7e3f7c5e7f317d3abc3ad00bdd5938636086348950f2116bafab540e13b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.04110",
    "kind": "arxiv",
    "version": 4
  }
}