Pith Number

pith:5AV4RJ4L

pith:2015:5AV4RJ4LA5VIGKESMI7I2C5CNZ

not attested not anchored not stored refs pending

The distribution of zeros of $\zeta'(s)$ and gaps between zeros of $\zeta(s)$

Fan Ge

arxiv:1510.04359 v1 · 2015-10-15 · 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{5AV4RJ4LA5VIGKESMI7I2C5CNZ}

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	2026-05-18T01:30:07.402239Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e82bc8a78b076a832892623e8d0ba26e413172393474c7d93157d9be0a01a8a2

Aliases

arxiv: 1510.04359 · arxiv_version: 1510.04359v1 · doi: 10.48550/arxiv.1510.04359 · pith_short_12: 5AV4RJ4LA5VI · pith_short_16: 5AV4RJ4LA5VIGKES · pith_short_8: 5AV4RJ4L

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/5AV4RJ4LA5VIGKESMI7I2C5CNZ \
  | 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: e82bc8a78b076a832892623e8d0ba26e413172393474c7d93157d9be0a01a8a2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bf27ee67d5d2d7d9fecbe4c9ed80af82f885279e9816b1c102b91a1305a2771c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-10-15T00:20:35Z",
    "title_canon_sha256": "ab04c42ff51750368ff8eb9b232fc710836608733b79f838285786898833159c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.04359",
    "kind": "arxiv",
    "version": 1
  }
}