Pith Number

pith:GC24SXDI

pith:2026:GC24SXDIE6B7Z7LXPUQ2VX2QZB

not attested not anchored not stored refs pending

An Optimal Analysis of the Product Test

Fernando Granha Jeronimo, Jacob Beckey, Pei Wu

arxiv:2607.21477 v1 · 2026-07-23 · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GC24SXDIE6B7Z7LXPUQ2VX2QZB}

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	2026-07-24T01:24:34.978459Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

30b5c95c682783fcfd777d21aadf50c846e73a58d1ee757c53a92dbc97e04f56

Aliases

arxiv: 2607.21477 · arxiv_version: 2607.21477v1 · doi: 10.48550/arxiv.2607.21477 · pith_short_12: GC24SXDIE6B7 · pith_short_16: GC24SXDIE6B7Z7LX · pith_short_8: GC24SXDI

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/GC24SXDIE6B7Z7LXPUQ2VX2QZB \
  | 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: 30b5c95c682783fcfd777d21aadf50c846e73a58d1ee757c53a92dbc97e04f56

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3cde559c261b1fbe2917f4ea07c7e1ca38f1f5473e2f957236c4a748cb4ec769",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-07-23T16:17:44Z",
    "title_canon_sha256": "7d0c4d988b1b7cec5affc221f4f2947027361cfa618a5c435b041db007cedfe4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.21477",
    "kind": "arxiv",
    "version": 1
  }
}