Pith Number

pith:67OFQSB4

pith:2015:67OFQSB4MXDH2KJSALZVCDIHLD

not attested not anchored not stored refs pending

A Generalization of Euler's Criterion to Composite Moduli

J\'ozsef Vass

arxiv:1507.00098 v1 · 2015-07-01 · 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{67OFQSB4MXDH2KJSALZVCDIHLD}

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	2026-05-18T01:37:30.554977Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f7dc58483c65c67d293202f3510d0758f8f00225dc126427074ae4a5417a6598

Aliases

arxiv: 1507.00098 · arxiv_version: 1507.00098v1 · doi: 10.48550/arxiv.1507.00098 · pith_short_12: 67OFQSB4MXDH · pith_short_16: 67OFQSB4MXDH2KJS · pith_short_8: 67OFQSB4

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/67OFQSB4MXDH2KJSALZVCDIHLD \
  | 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: f7dc58483c65c67d293202f3510d0758f8f00225dc126427074ae4a5417a6598

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1dc9ed2424d51efb907b2c931e17f696267e49a430cd8fab8afb7ac25426dc14",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-07-01T03:27:50Z",
    "title_canon_sha256": "a6b6f7c224bd5b6b9838928ad1359947231843792abb0f65663504ab5d1b3187"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.00098",
    "kind": "arxiv",
    "version": 1
  }
}