Pith Number

pith:FVFHNOS4

pith:2016:FVFHNOS4WLBR24PU77EVWWQ2JA

not attested not anchored not stored refs pending

Quantifying the degree of average contraction of Collatz orbits

Duccio Fanelli, Timoteo Carletti

arxiv:1612.07820 v1 · 2016-12-21 · math.DS · cond-mat.other · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FVFHNOS4WLBR24PU77EVWWQ2JA}

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	2026-05-18T00:53:57.278685Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2d4a76ba5cb2c31d71f4ffc95b5a1a481c3b16f6e05183d865cb9a0c286dfe80

Aliases

arxiv: 1612.07820 · arxiv_version: 1612.07820v1 · doi: 10.48550/arxiv.1612.07820 · pith_short_12: FVFHNOS4WLBR · pith_short_16: FVFHNOS4WLBR24PU · pith_short_8: FVFHNOS4

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/FVFHNOS4WLBR24PU77EVWWQ2JA \
  | 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: 2d4a76ba5cb2c31d71f4ffc95b5a1a481c3b16f6e05183d865cb9a0c286dfe80

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c028883c6cb3e6d4dfa0abb4063040fb59c43c97acee7251881b13c7314186f1",
    "cross_cats_sorted": [
      "cond-mat.other",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2016-12-21T22:38:02Z",
    "title_canon_sha256": "f93d31871869dffbd532d05c2a22366f683a321f46a8f3b1ee3b960eecd143b6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.07820",
    "kind": "arxiv",
    "version": 1
  }
}