Pith Number

pith:NRCGEVHL

pith:2002:NRCGEVHLGUSZYRSSBA4JIDQAFG

not attested not anchored not stored refs pending

Bounds for the 3x+1 Problem using Difference Inequalities

Ilia Krasikov, Jeffrey C. Lagarias

arxiv:math/0205002 v1 · 2002-04-30 · 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{NRCGEVHLGUSZYRSSBA4JIDQAFG}

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	2026-05-18T01:38:29.597400Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6c446254eb35259c46520838940e0029af2acf901345956ce0cd8df40d5a5930

Aliases

arxiv: math/0205002 · arxiv_version: math/0205002v1 · doi: 10.48550/arxiv.math/0205002 · pith_short_12: NRCGEVHLGUSZ · pith_short_16: NRCGEVHLGUSZYRSS · pith_short_8: NRCGEVHL

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/NRCGEVHLGUSZYRSSBA4JIDQAFG \
  | 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: 6c446254eb35259c46520838940e0029af2acf901345956ce0cd8df40d5a5930

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6806b9709ef53326b0d8bf3b678cce75a6acf30ff4cf2048d7c8122322763b3b",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2002-04-30T21:57:00Z",
    "title_canon_sha256": "c1c336037cab4fe32a8d29e57358112412429d6c57f082e446960e6bb7f7e513"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0205002",
    "kind": "arxiv",
    "version": 1
  }
}