Pith Number

pith:TXC4C6Y6

pith:2025:TXC4C6Y66XUTVM7YPIUML754UW

not attested not anchored not stored refs pending

Characterizing Small Circuit Classes from FAC^0 to FAC^1 via Discrete Ordinary Differential Equations

Arnaud Durand, Juha Kontinen, Melissa Antonelli

arxiv:2506.23404 v1 · 2025-06-29 · cs.CC · cs.LO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TXC4C6Y66XUTVM7YPIUML754UW}

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	2026-07-05T11:29:21.099252Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9dc5c17b1ef5e93ab3f87a28c5ffbca5be29d3bb6bab3f0402f31de5c99c8731

Aliases

arxiv: 2506.23404 · arxiv_version: 2506.23404v1 · doi: 10.48550/arxiv.2506.23404 · pith_short_12: TXC4C6Y66XUT · pith_short_16: TXC4C6Y66XUTVM7Y · pith_short_8: TXC4C6Y6

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/TXC4C6Y66XUTVM7YPIUML754UW \
  | 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: 9dc5c17b1ef5e93ab3f87a28c5ffbca5be29d3bb6bab3f0402f31de5c99c8731

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bf32d54334374424f9b146748d5c3d27cc6263406d3b940ba92615dfb3157768",
    "cross_cats_sorted": [
      "cs.LO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2025-06-29T21:31:12Z",
    "title_canon_sha256": "83325b4fd8dea104742657af92fb50b4dab657e1fbfa242372be38a2fb03ce0a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.23404",
    "kind": "arxiv",
    "version": 1
  }
}