Pith Number

pith:ZP6UXPBO

pith:2011:ZP6UXPBO4BXVLRBRWMBJLYUM6W

not attested not anchored not stored refs pending

Geometric configurations in the ring of integers modulo $p^{\ell}$

Alex Iosevich, David Covert, Jonathan Pakianathan

arxiv:1105.5373 v1 · 2011-05-26 · math.CO · math.CA · 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{ZP6UXPBO4BXVLRBRWMBJLYUM6W}

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	2026-05-18T04:21:12.662725Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cbfd4bbc2ee06f55c431b30295e28cf5a2d3a884317007ad638cfb50e8f4c48c

Aliases

arxiv: 1105.5373 · arxiv_version: 1105.5373v1 · doi: 10.48550/arxiv.1105.5373 · pith_short_12: ZP6UXPBO4BXV · pith_short_16: ZP6UXPBO4BXVLRBR · pith_short_8: ZP6UXPBO

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/ZP6UXPBO4BXVLRBRWMBJLYUM6W \
  | 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: cbfd4bbc2ee06f55c431b30295e28cf5a2d3a884317007ad638cfb50e8f4c48c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e93f4907118ae5916b07756da3a2cd24350490811818bcd74e588c546d15ccb6",
    "cross_cats_sorted": [
      "math.CA",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-05-26T18:59:40Z",
    "title_canon_sha256": "8ecc07f16ff41d6c6d1b2089085a451857b0a92254847e3f68a6293a4dec4d96"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.5373",
    "kind": "arxiv",
    "version": 1
  }
}