Pith Number

pith:HLTLF7IC

pith:2019:HLTLF7ICXQXMJAEGO7PVJAQPRG

not attested not anchored not stored refs pending

Almost all orbits of the Collatz map attain almost bounded values

Terence Tao

arxiv:1909.03562 v5 · 2019-09-08 · math.PR · math.DS · 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{HLTLF7ICXQXMJAEGO7PVJAQPRG}

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

Parity vectors and paradoxical sequences in the accelerated Collatz map

Receipt and verification

First computed	2026-07-05T03:57:22.924048Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3ae6b2fd02bc2ec4808677df54820f89888ff657894712099c0c12de876a1fbb

Aliases

arxiv: 1909.03562 · arxiv_version: 1909.03562v5 · doi: 10.48550/arxiv.1909.03562 · pith_short_12: HLTLF7ICXQXM · pith_short_16: HLTLF7ICXQXMJAEG · pith_short_8: HLTLF7IC

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/HLTLF7ICXQXMJAEGO7PVJAQPRG \
  | 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: 3ae6b2fd02bc2ec4808677df54820f89888ff657894712099c0c12de876a1fbb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "114db7c451063f7e9187141fb39ccb6d35a416fb1819bc51efe35c0db34cc352",
    "cross_cats_sorted": [
      "math.DS",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2019-09-08T23:15:50Z",
    "title_canon_sha256": "947882557cdcebe03e124f89c4867e647c8c6165d7952996aee5be3dad0bc3c0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1909.03562",
    "kind": "arxiv",
    "version": 5
  }
}