Pith Number

pith:NWOCLN3Z

pith:2011:NWOCLN3ZWC5KCU6THIWT34JEQN

not attested not anchored not stored refs pending

Size of orthogonal sets of exponentials for the disk

Alex Iosevich, Mihail N. Kolountzakis

arxiv:1111.1357 v1 · 2011-11-05 · math.CA · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NWOCLN3ZWC5KCU6THIWT34JEQN}

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	2026-05-18T04:09:26.393667Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6d9c25b779b0baa153d33a2d3df1248342bf89066d5d21f31126f66fa95a8a62

Aliases

arxiv: 1111.1357 · arxiv_version: 1111.1357v1 · doi: 10.48550/arxiv.1111.1357 · pith_short_12: NWOCLN3ZWC5K · pith_short_16: NWOCLN3ZWC5KCU6T · pith_short_8: NWOCLN3Z

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/NWOCLN3ZWC5KCU6THIWT34JEQN \
  | 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: 6d9c25b779b0baa153d33a2d3df1248342bf89066d5d21f31126f66fa95a8a62

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d20e8f31ea1c186d7422634c7806b6bd0e3020f9beef40252d522a28e3817fae",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2011-11-05T22:16:34Z",
    "title_canon_sha256": "4be278327c25262939da37a671ec529bcc356568bb24c0b465de7c175a68e9dc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.1357",
    "kind": "arxiv",
    "version": 1
  }
}