Pith Number

pith:4SU5IZRN

pith:2016:4SU5IZRNJHLWJWURAOGG7TW3ZP

not attested not anchored not stored refs pending

Geometric properties of the Markov and Lagrange spectra

Carlos Gustavo Moreira

arxiv:1612.05782 v4 · 2016-12-17 · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4SU5IZRNJHLWJWURAOGG7TW3ZP}

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	2026-05-18T00:18:32.024869Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e4a9d4662d49d764da91038c6fcedbcbf0ff28a15780bd2d90d190d385d1d878

Aliases

arxiv: 1612.05782 · arxiv_version: 1612.05782v4 · doi: 10.48550/arxiv.1612.05782 · pith_short_12: 4SU5IZRNJHLW · pith_short_16: 4SU5IZRNJHLWJWUR · pith_short_8: 4SU5IZRN

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/4SU5IZRNJHLWJWURAOGG7TW3ZP \
  | 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: e4a9d4662d49d764da91038c6fcedbcbf0ff28a15780bd2d90d190d385d1d878

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "16272536e68b9aa7f89f146703dd732b076f0917958f1f5d680f9469c18d66ae",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-12-17T15:34:55Z",
    "title_canon_sha256": "82d6aa479fcedf9d7de149c65874b48f011e87e655e4ae19d648d882bf8b1f8d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.05782",
    "kind": "arxiv",
    "version": 4
  }
}