Pith Number

pith:PXDKZJUA

pith:2026:PXDKZJUAKMWI4W7SJDXMVWQEMH

not attested not anchored not stored refs pending

Logical Undefinability of the Generalized Collatz Transition Relation in B\"uchi Arithmetic

Madhav Dhiman, Rohan Pandey

arxiv:2601.12772 v2 · 2026-01-19 · math.NT · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PXDKZJUAKMWI4W7SJDXMVWQEMH}

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	2026-06-09T02:07:17.715280Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7dc6aca680532c8e5bf248eecada0461f0fbab240835082882417c0e224e91c3

Aliases

arxiv: 2601.12772 · arxiv_version: 2601.12772v2 · doi: 10.48550/arxiv.2601.12772 · pith_short_12: PXDKZJUAKMWI · pith_short_16: PXDKZJUAKMWI4W7S · pith_short_8: PXDKZJUA

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/PXDKZJUAKMWI4W7SJDXMVWQEMH \
  | 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: 7dc6aca680532c8e5bf248eecada0461f0fbab240835082882417c0e224e91c3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d6b6ee13279f9e56b0b56cee56d2eb17f3dd991cd3a532c0abd287b6f3b022b9",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-01-19T07:01:00Z",
    "title_canon_sha256": "810be92e4fb6e7a857556282fac22921406ece7e749fb247798d524988309ab4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.12772",
    "kind": "arxiv",
    "version": 2
  }
}