Pith Number

pith:MQHQG2RO

pith:2019:MQHQG2RO6CLDMJE3X7X7I5KFW3

not attested not anchored not stored refs pending

Integer patterns in Collatz sequences

Zenon B. Batang

arxiv:1907.07088 v2 · 2019-07-14 · 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{MQHQG2RO6CLDMJE3X7X7I5KFW3}

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	2026-05-17T23:40:22.924932Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

640f036a2ef09636249bbfeff47545b6df46600a4b0af4601788882995481170

Aliases

arxiv: 1907.07088 · arxiv_version: 1907.07088v2 · doi: 10.48550/arxiv.1907.07088 · pith_short_12: MQHQG2RO6CLD · pith_short_16: MQHQG2RO6CLDMJE3 · pith_short_8: MQHQG2RO

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/MQHQG2RO6CLDMJE3X7X7I5KFW3 \
  | 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: 640f036a2ef09636249bbfeff47545b6df46600a4b0af4601788882995481170

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5028549c8423813084ed4db288830343ac3b076f978b48bcc09fbabf7e3b810e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GM",
    "submitted_at": "2019-07-14T21:37:14Z",
    "title_canon_sha256": "5781c829b69bdf5bd30035294741265afe6b4ebae47c904eb79540b45a6ff089"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1907.07088",
    "kind": "arxiv",
    "version": 2
  }
}