Pith Number

pith:NRGZ3WY7

pith:2012:NRGZ3WY7IPRJT53NYK2WJL4WHD

not attested not anchored not stored refs pending

Hasse principle for G-trace forms

E. Bayer-Fluckiger, J-P. Serre, R. Parimala

arxiv:1210.5765 v2 · 2012-10-21 · 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{NRGZ3WY7IPRJT53NYK2WJL4WHD}

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	2026-05-18T01:53:45.269237Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6c4d9ddb1f43e299f76dc2b564af9638f4fc8a8c7ae80809521bc058da77f039

Aliases

arxiv: 1210.5765 · arxiv_version: 1210.5765v2 · doi: 10.48550/arxiv.1210.5765 · pith_short_12: NRGZ3WY7IPRJ · pith_short_16: NRGZ3WY7IPRJT53N · pith_short_8: NRGZ3WY7

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/NRGZ3WY7IPRJT53NYK2WJL4WHD \
  | 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: 6c4d9ddb1f43e299f76dc2b564af9638f4fc8a8c7ae80809521bc058da77f039

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ce6b0f6b1e1ccebebdb3f83799b6666e07ba5f5dc197befeb30a1f0d937e11e5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-10-21T21:40:53Z",
    "title_canon_sha256": "0e5134b29bffa2357708d9baf9beb517cf767e61353a95fbc06ff9829969031c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.5765",
    "kind": "arxiv",
    "version": 2
  }
}