Pith Number

pith:RF3D35YE

pith:2025:RF3D35YEXZAWSOBV2L7CI42CD2

not attested not anchored not stored refs pending

Spectrality of a measure consisting of two line segments

Mihail N. Kolountzakis, Sha Wu

arxiv:2501.11367 v2 · 2025-01-20 · 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{RF3D35YEXZAWSOBV2L7CI42CD2}

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.

Cited by

1 paper in Pith

Frame bound, spectral gap and Plus space

Receipt and verification

First computed	2026-07-05T10:06:10.483101Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

89763df704be41693835d2fe2473421ebda6bcfc3572ab74f29c7d7312f1fa89

Aliases

arxiv: 2501.11367 · arxiv_version: 2501.11367v2 · doi: 10.48550/arxiv.2501.11367 · pith_short_12: RF3D35YEXZAW · pith_short_16: RF3D35YEXZAWSOBV · pith_short_8: RF3D35YE

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/RF3D35YEXZAWSOBV2L7CI42CD2 \
  | 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: 89763df704be41693835d2fe2473421ebda6bcfc3572ab74f29c7d7312f1fa89

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b3c3eb521eecb76f70ccc608747f4a0498ae0e5fe309dee2840f88afb1e44512",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2025-01-20T09:56:13Z",
    "title_canon_sha256": "47649a2c774fe81f2d170f5a3c709abd695a7ae7634f2f7c9ad4e80c5e9dc798"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2501.11367",
    "kind": "arxiv",
    "version": 2
  }
}