Pith Number

pith:4MXBLHDI

pith:2013:4MXBLHDIDZBF6F7WIRYFGLHWRF

not attested not anchored not stored refs pending

A generalization of Schur's theorem and its application to consecutive power residues

Carsten Dietzel

arxiv:1309.7506 v1 · 2013-09-28 · 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{4MXBLHDIDZBF6F7WIRYFGLHWRF}

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	2026-05-18T03:11:56.810393Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e32e159c681e425f17f64470532cf6895268eff07cd256eb55fa857ced8a2b37

Aliases

arxiv: 1309.7506 · arxiv_version: 1309.7506v1 · doi: 10.48550/arxiv.1309.7506 · pith_short_12: 4MXBLHDIDZBF · pith_short_16: 4MXBLHDIDZBF6F7W · pith_short_8: 4MXBLHDI

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/4MXBLHDIDZBF6F7WIRYFGLHWRF \
  | 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: e32e159c681e425f17f64470532cf6895268eff07cd256eb55fa857ced8a2b37

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1b7acb2b65680c33fcb94ce3e652a43f0fd814a63b266d6462609f6ca2a9306f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-09-28T21:49:09Z",
    "title_canon_sha256": "2f0e969062a13b3b500158d3a99902d65effa00c78f3b852321af81af26778a1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.7506",
    "kind": "arxiv",
    "version": 1
  }
}