Pith Number

pith:LGJ77L5R

pith:2024:LGJ77L5RU7TZEDUIVG36ZEDT5N

not attested not anchored not stored refs pending

Expansions of real numbers in non-integer bases and charaterisation of Lazy expansion of 1

Vorashil Farzaliyev

arxiv:2412.10378 v1 · 2024-11-27 · math.GM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LGJ77L5RU7TZEDUIVG36ZEDT5N}

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	2026-07-05T09:49:15.002481Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5993ffafb1a7e7920e88a9b7ec9073eb661b2160efe08ef1861f5629482675e1

Aliases

arxiv: 2412.10378 · arxiv_version: 2412.10378v1 · doi: 10.48550/arxiv.2412.10378 · pith_short_12: LGJ77L5RU7TZ · pith_short_16: LGJ77L5RU7TZEDUI · pith_short_8: LGJ77L5R

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/LGJ77L5RU7TZEDUIVG36ZEDT5N \
  | 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: 5993ffafb1a7e7920e88a9b7ec9073eb661b2160efe08ef1861f5629482675e1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eb0aa154a79dca2736048638848c2666eb0cd04d6c56678e06c0bd5a2104ee64",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GM",
    "submitted_at": "2024-11-27T01:02:19Z",
    "title_canon_sha256": "d0b90edaee41b41d0247aa18c9c6a9f0b43726d6194ae468da4606c937c5d629"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.10378",
    "kind": "arxiv",
    "version": 1
  }
}