Pith Number

pith:VNZMGIVD

pith:2012:VNZMGIVDX2EG7NQ5TLYVTLYGDX

not attested not anchored not stored refs pending

Non universality on the critical line

Johan Andersson

arxiv:1207.4927 v2 · 2012-07-20 · 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{VNZMGIVDX2EG7NQ5TLYVTLYGDX}

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	2026-05-18T01:12:43.658312Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ab72c322a3be886fb61d9af159af061dfcbc364308d04e5a7a05196d86d60fd7

Aliases

arxiv: 1207.4927 · arxiv_version: 1207.4927v2 · doi: 10.48550/arxiv.1207.4927 · pith_short_12: VNZMGIVDX2EG · pith_short_16: VNZMGIVDX2EG7NQ5 · pith_short_8: VNZMGIVD

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/VNZMGIVDX2EG7NQ5TLYVTLYGDX \
  | 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: ab72c322a3be886fb61d9af159af061dfcbc364308d04e5a7a05196d86d60fd7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ebc46a550e4deed76df8dad4b3d0c128d517c023c4d623b6e33000cd5af181c3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-07-20T11:56:11Z",
    "title_canon_sha256": "ee90ce88b12a96b53ed3f14c6a09898e1f701655bb1e333158cc5e98fed9a26b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.4927",
    "kind": "arxiv",
    "version": 2
  }
}