Pith Number

pith:SD2B4QIA

pith:2013:SD2B4QIA45MFDTIK6XDJZCM4AT

not attested not anchored not stored refs pending

Multiple lattice tiles and Riesz bases of exponentials

Mihail N. Kolountzakis

arxiv:1305.2632 v1 · 2013-05-12 · 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{SD2B4QIA45MFDTIK6XDJZCM4AT}

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	2026-05-18T03:25:57.361356Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

90f41e4100e75851cd0af5c69c899c04c263dfd9954792699c8f90dca475b670

Aliases

arxiv: 1305.2632 · arxiv_version: 1305.2632v1 · doi: 10.48550/arxiv.1305.2632 · pith_short_12: SD2B4QIA45MF · pith_short_16: SD2B4QIA45MFDTIK · pith_short_8: SD2B4QIA

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/SD2B4QIA45MFDTIK6XDJZCM4AT \
  | 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: 90f41e4100e75851cd0af5c69c899c04c263dfd9954792699c8f90dca475b670

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6696d7f8294f5b98e157be1e7b64ec579128cd95c4cecbcf7ee821059b8fdc32",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2013-05-12T21:01:10Z",
    "title_canon_sha256": "6801bba2ed9a3b5326ea5090cd89fe4b66905e2643338ea2596801cd4e728bc6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.2632",
    "kind": "arxiv",
    "version": 1
  }
}