Pith Number

pith:5B6OMON2

pith:2024:5B6OMON2YHRK7FNQXFXIRVTFUN

not attested not anchored not stored refs pending

An approximation of the Collatz map and a lower bound for the average total stopping time

Manuel Inselmann

arxiv:2402.03276 v3 · 2024-02-05 · math.DS · math.CO · math.NT · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5B6OMON2YHRK7FNQXFXIRVTFUN}

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.

Cited by

1 paper in Pith

Efficient Computation of Collatz Sequence Stopping Times: A Novel Algorithmic Approach

Receipt and verification

First computed	2026-07-05T08:54:46.978114Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e87ce639bac1e2af95b0b96e88d665a351ab0298d0abe8b9b46b0d8e2e91d06d

Aliases

arxiv: 2402.03276 · arxiv_version: 2402.03276v3 · doi: 10.48550/arxiv.2402.03276 · pith_short_12: 5B6OMON2YHRK · pith_short_16: 5B6OMON2YHRK7FNQ · pith_short_8: 5B6OMON2

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/5B6OMON2YHRK7FNQXFXIRVTFUN \
  | 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: e87ce639bac1e2af95b0b96e88d665a351ab0298d0abe8b9b46b0d8e2e91d06d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "61ecdb902e3e3c8f11c3b67418031d05dff6458b0b7429d82f17bd1f0a11284c",
    "cross_cats_sorted": [
      "math.CO",
      "math.NT",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2024-02-05T18:34:02Z",
    "title_canon_sha256": "69324be9d7df9ca577e76a83527de1222b340faf0be5859e538dcae1b3ea0dec"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2402.03276",
    "kind": "arxiv",
    "version": 3
  }
}