Pith Number

pith:AS4R3LJG

pith:2026:AS4R3LJGFQR3PJKI4LX3WFKSOH

not attested not anchored not stored refs pending

Recursion and proof theoretical characterizations of small circuit classes with modulo counting via discrete differential equations (long version)

Arnaud Durand, Melissa Antonelli, Rui Li

arxiv:2605.23805 v1 · 2026-05-22 · 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{AS4R3LJGFQR3PJKI4LX3WFKSOH}

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	2026-05-25T02:02:33.329785Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

04b91dad262c23b7a548e2efbb155271d7798953f991d2a7139a7b62f801eece

Aliases

arxiv: 2605.23805 · arxiv_version: 2605.23805v1 · doi: 10.48550/arxiv.2605.23805 · pith_short_12: AS4R3LJGFQR3 · pith_short_16: AS4R3LJGFQR3PJKI · pith_short_8: AS4R3LJG

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/AS4R3LJGFQR3PJKI4LX3WFKSOH \
  | 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: 04b91dad262c23b7a548e2efbb155271d7798953f991d2a7139a7b62f801eece

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ee1e927bcde2e8d5f306fc0a3c7f9a497de0bcf1eff806ca53f3657ec6c770a8",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2026-05-22T16:06:37Z",
    "title_canon_sha256": "4f38513177d2695c7668bdb2604b01711fc589a1e05f764bc8e09aab6a47fbb7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.23805",
    "kind": "arxiv",
    "version": 1
  }
}