Pith Number

pith:4FBFJOME

pith:2013:4FBFJOME75ESJGVQVR3KDFSASC

not attested not anchored not stored refs pending

On quadratic irrationals with bounded partial quotients

Jean Bourgain

arxiv:1311.5909 v2 · 2013-11-22 · 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{4FBFJOME75ESJGVQVR3KDFSASC}

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	2026-05-18T01:09:38.322930Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e14254b984ff49249ab0ac76a1964090bea069a5b6803101a7a2a0865057b27a

Aliases

arxiv: 1311.5909 · arxiv_version: 1311.5909v2 · doi: 10.48550/arxiv.1311.5909 · pith_short_12: 4FBFJOME75ES · pith_short_16: 4FBFJOME75ESJGVQ · pith_short_8: 4FBFJOME

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/4FBFJOME75ESJGVQVR3KDFSASC \
  | 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: e14254b984ff49249ab0ac76a1964090bea069a5b6803101a7a2a0865057b27a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2eb7f8615354d59d65e547fc8b2376707645a4169e66fc1b311e3f2436cff6d6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-11-22T21:38:48Z",
    "title_canon_sha256": "e5832dd79b59f66d038ca5721e3183d1ab6940396b8731726d5984e942a5ba18"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.5909",
    "kind": "arxiv",
    "version": 2
  }
}