Pith Number

pith:O3F7CMHS

pith:2007:O3F7CMHSQ4LJYRDASD4RXFUGGT

not attested not anchored not stored refs pending

A Symplectic Test of the L-Functions Ratios Conjecture

Steven J. Miller

arxiv:0704.0927 v5 · 2007-04-06 · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{O3F7CMHSQ4LJYRDASD4RXFUGGT}

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	2026-05-18T04:41:04.099183Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

76cbf130f287169c446090f91b968634ec34d216e12eb557508e25feb799d546

Aliases

arxiv: 0704.0927 · arxiv_version: 0704.0927v5 · doi: 10.48550/arxiv.0704.0927 · pith_short_12: O3F7CMHSQ4LJ · pith_short_16: O3F7CMHSQ4LJYRDA · pith_short_8: O3F7CMHS

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/O3F7CMHSQ4LJYRDASD4RXFUGGT \
  | 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: 76cbf130f287169c446090f91b968634ec34d216e12eb557508e25feb799d546

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4bda51f585321487bb74624e733dd713a3b752b68ee2d3ebbae7ad017f45ea31",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2007-04-06T19:59:58Z",
    "title_canon_sha256": "8569a9c2e5eb2e23bc5920cb17497a4bf9fa88ec87cc9168373b134fc4398b41"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0704.0927",
    "kind": "arxiv",
    "version": 5
  }
}