Pith Number

pith:PISA5JV4

pith:2026:PISA5JV4B5LICTEYYYODLOT6PD

not attested not anchored not stored refs pending

A Lower Bound for Read-Once Parity Branching Programs

Ben lee Volk

arxiv:2607.05944 v1 · 2026-07-07 · 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{PISA5JV4B5LICTEYYYODLOT6PD}

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	2026-07-08T01:18:51.171180Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a240ea6bc0f56814c98c61c35ba7e78e36a6cae8d6b5cedd075edc000d83b10

Aliases

arxiv: 2607.05944 · arxiv_version: 2607.05944v1 · doi: 10.48550/arxiv.2607.05944 · pith_short_12: PISA5JV4B5LI · pith_short_16: PISA5JV4B5LICTEY · pith_short_8: PISA5JV4

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/PISA5JV4B5LICTEYYYODLOT6PD \
  | 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: 7a240ea6bc0f56814c98c61c35ba7e78e36a6cae8d6b5cedd075edc000d83b10

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d1d4252feb0a4b093b4130e9cad6b42b420daed4d180a8a4ae5b776ed3b87e48",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2026-07-07T07:43:30Z",
    "title_canon_sha256": "197272132f1e5915be0fee5781fce8e46e60a9e03f1cacfaf663fc13c7d69069"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.05944",
    "kind": "arxiv",
    "version": 1
  }
}