Pith Number

pith:7RDULEP7

pith:2013:7RDULEP7OOIDNMY7AZO6LQDCK3

not attested not anchored not stored refs pending

A sum rule for the critical zeros of $\zeta(s)$

M.L. Glasser

arxiv:1309.7040 v1 · 2013-09-25 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7RDULEP7OOIDNMY7AZO6LQDCK3}

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	2026-05-18T03:12:08.214167Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fc474591ff739036b31f065de5c06256cea874e92b22aedd8a99b24dcff2e856

Aliases

arxiv: 1309.7040 · arxiv_version: 1309.7040v1 · doi: 10.48550/arxiv.1309.7040 · pith_short_12: 7RDULEP7OOID · pith_short_16: 7RDULEP7OOIDNMY7 · pith_short_8: 7RDULEP7

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/7RDULEP7OOIDNMY7AZO6LQDCK3 \
  | 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: fc474591ff739036b31f065de5c06256cea874e92b22aedd8a99b24dcff2e856

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0ae4c01f2acf35aa0436afbe76a1f04d37b0956693410e1427d293beaaff55be",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2013-09-25T23:29:25Z",
    "title_canon_sha256": "2fee68916c8d1f443817f113088f835e60e31371da6ebbbefd4529761447fff4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.7040",
    "kind": "arxiv",
    "version": 1
  }
}