Pith Number

pith:M3DKLGVK

pith:2011:M3DKLGVKSTUS7WES7YLZKT3ZF6

not attested not anchored not stored refs pending

On the Modulus of a Union of Nested Annuli

Mark Comerford

arxiv:1108.4620 v2 · 2011-08-23 · math.CV

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{M3DKLGVKSTUS7WES7YLZKT3ZF6}

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	2026-05-18T04:14:46.965731Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

66c6a59aaa94e92fd892fe17954f792f8488a72491ebc0f164df43811523f4e2

Aliases

arxiv: 1108.4620 · arxiv_version: 1108.4620v2 · doi: 10.48550/arxiv.1108.4620 · pith_short_12: M3DKLGVKSTUS · pith_short_16: M3DKLGVKSTUS7WES · pith_short_8: M3DKLGVK

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/M3DKLGVKSTUS7WES7YLZKT3ZF6 \
  | 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: 66c6a59aaa94e92fd892fe17954f792f8488a72491ebc0f164df43811523f4e2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6f4fc8d9a627b15a5c4432a3266c1fc3a28b380632fe769db9f11731dfddbb44",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2011-08-23T14:51:39Z",
    "title_canon_sha256": "3e32bbea88dccdbeb6e23d6c8dcef0d80a23b2f712aa3a754bbf3f0358c43c5b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.4620",
    "kind": "arxiv",
    "version": 2
  }
}