Pith Number

pith:LBIYR54V

pith:2012:LBIYR54VZOJSH4PXM34OIJGX3D

not attested not anchored not stored refs pending

Bubbles of congruent primes

Frank Thorne

arxiv:1201.5400 v1 · 2012-01-25 · 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{LBIYR54VZOJSH4PXM34OIJGX3D}

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	2026-05-17T23:53:36.342218Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

585188f795cb9323f1f766f8e424d7d8fe6cf3b7f52aaca4e0d08ea454472031

Aliases

arxiv: 1201.5400 · arxiv_version: 1201.5400v1 · doi: 10.48550/arxiv.1201.5400 · pith_short_12: LBIYR54VZOJS · pith_short_16: LBIYR54VZOJSH4PX · pith_short_8: LBIYR54V

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/LBIYR54VZOJSH4PXM34OIJGX3D \
  | 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: 585188f795cb9323f1f766f8e424d7d8fe6cf3b7f52aaca4e0d08ea454472031

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bb39f7edfa2b8930f6bc4676611bda431994a8ad3f6f260da5214920cbb043e5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-01-25T21:38:53Z",
    "title_canon_sha256": "b54e8c6cd3fd58134a20dbd917f41e721473b3429cac299f1d4735269856f47d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.5400",
    "kind": "arxiv",
    "version": 1
  }
}