Pith Number

pith:ASCT5SOK

pith:2017:ASCT5SOKPPQVU3XCK7XJDNPQJP

not attested not anchored not stored refs pending

The structure of multiplicative tilings of the real line

Mihail N. Kolountzakis, Yang Wang

arxiv:1710.03108 v1 · 2017-10-09 · 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{ASCT5SOKPPQVU3XCK7XJDNPQJP}

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	2026-05-18T00:33:27.048358Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

04853ec9ca7be15a6ee257ee91b5f04bc8457dae5863e92cf8335ddb4844577b

Aliases

arxiv: 1710.03108 · arxiv_version: 1710.03108v1 · doi: 10.48550/arxiv.1710.03108 · pith_short_12: ASCT5SOKPPQV · pith_short_16: ASCT5SOKPPQVU3XC · pith_short_8: ASCT5SOK

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/ASCT5SOKPPQVU3XCK7XJDNPQJP \
  | 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: 04853ec9ca7be15a6ee257ee91b5f04bc8457dae5863e92cf8335ddb4844577b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f4ecb199d10b330f9a4427a1e754209fb212c6a56cbbe2b63ea8adc0c33521a6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2017-10-09T14:12:49Z",
    "title_canon_sha256": "2ca48f96ed1f2afbfa95a8a76a6cbcdf16103fbb3f905b818c3acdf1d59050fa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1710.03108",
    "kind": "arxiv",
    "version": 1
  }
}