Pith Number

pith:3GPODXKD

pith:2011:3GPODXKDM6HYYULYKATOH5POY2

not attested not anchored not stored refs pending

Periodicity of the spectrum of a finite union of intervals

Mihail N. Kolountzakis

arxiv:1102.5557 v1 · 2011-02-27 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3GPODXKDM6HYYULYKATOH5POY2}

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	2026-05-18T04:27:46.571809Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d99ee1dd43678f8c51785026e3f5eec686c60a2501b281c471f70643bc5f4f10

Aliases

arxiv: 1102.5557 · arxiv_version: 1102.5557v1 · doi: 10.48550/arxiv.1102.5557 · pith_short_12: 3GPODXKDM6HY · pith_short_16: 3GPODXKDM6HYYULY · pith_short_8: 3GPODXKD

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/3GPODXKDM6HYYULYKATOH5POY2 \
  | 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: d99ee1dd43678f8c51785026e3f5eec686c60a2501b281c471f70643bc5f4f10

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "17e3261e4d5b426b9d1992f37b482e5ef7ed7a32f6b60fae15a8e5e908cee281",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2011-02-27T22:43:09Z",
    "title_canon_sha256": "0a9de0094727386119492d8b9be8864f452f4ed0fac1ead1263746accbb504c7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.5557",
    "kind": "arxiv",
    "version": 1
  }
}