Pith Number

pith:5OBYB5DE

pith:2017:5OBYB5DEQPF3VYQRLIANMHUPHD

not attested not anchored not stored refs pending

Rationality of the zeta function of the subgroups of abelian $p$-groups

Olivier Ramar\'e

arxiv:1703.00684 v1 · 2017-03-02 · math.NT · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5OBYB5DEQPF3VYQRLIANMHUPHD}

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	2026-05-18T00:49:41.059441Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eb8380f46483cbbae2115a00d61e8f38f15f877c39b84ab94bfb086086ccfdca

Aliases

arxiv: 1703.00684 · arxiv_version: 1703.00684v1 · doi: 10.48550/arxiv.1703.00684 · pith_short_12: 5OBYB5DEQPF3 · pith_short_16: 5OBYB5DEQPF3VYQR · pith_short_8: 5OBYB5DE

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/5OBYB5DEQPF3VYQRLIANMHUPHD \
  | 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: eb8380f46483cbbae2115a00d61e8f38f15f877c39b84ab94bfb086086ccfdca

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "456b794ca74d410b094f6e0d5a212fc838d4e1a5423e92653fefa8125d2f563e",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2017-03-02T09:44:21Z",
    "title_canon_sha256": "652ec4de8b4cb76194b8c73985edd2fb1956c21b70fb1b0bfb75f13b9f20b15b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1703.00684",
    "kind": "arxiv",
    "version": 1
  }
}