Pith Number

pith:DUZA5FK3

pith:2015:DUZA5FK3UQJZOI2EQ6GIUPCRLP

not attested not anchored not stored refs pending

A Randomized Version of the Collatz $3x + 1$ Problem

Aristides V. Doumas, Vassilis G. Papanicolaou

arxiv:1503.03658 v1 · 2015-03-12 · math.PR · 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{DUZA5FK3UQJZOI2EQ6GIUPCRLP}

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	2026-05-18T02:24:27.704465Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1d320e955ba413972344878c8a3c515be1988918ae4dc8a8f3cea97cd15f4bd0

Aliases

arxiv: 1503.03658 · arxiv_version: 1503.03658v1 · doi: 10.48550/arxiv.1503.03658 · pith_short_12: DUZA5FK3UQJZ · pith_short_16: DUZA5FK3UQJZOI2E · pith_short_8: DUZA5FK3

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/DUZA5FK3UQJZOI2EQ6GIUPCRLP \
  | 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: 1d320e955ba413972344878c8a3c515be1988918ae4dc8a8f3cea97cd15f4bd0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6db66eae688ad0ba7629f8e5d561c34784708234b59f4f4c221d524946866eb2",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-03-12T10:05:52Z",
    "title_canon_sha256": "a7ea727509a635a51f7af9e22f7c7ddc83c41a4dd1116869f642567dd1214985"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.03658",
    "kind": "arxiv",
    "version": 1
  }
}