Pith Number

pith:I75TYNL7

pith:2011:I75TYNL7YMLO6UMIWAZXHU6C5V

not attested not anchored not stored refs pending

Contracting elements and random walks

Alessandro Sisto

arxiv:1112.2666 v2 · 2011-12-12 · math.GT · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{I75TYNL7YMLO6UMIWAZXHU6C5V}

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	2026-05-18T03:08:25.263834Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

47fb3c357fc316ef5188b03373d3c2ed7fae027d624702c461879bb6be6830b7

Aliases

arxiv: 1112.2666 · arxiv_version: 1112.2666v2 · doi: 10.48550/arxiv.1112.2666 · pith_short_12: I75TYNL7YMLO · pith_short_16: I75TYNL7YMLO6UMI · pith_short_8: I75TYNL7

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/I75TYNL7YMLO6UMIWAZXHU6C5V \
  | 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: 47fb3c357fc316ef5188b03373d3c2ed7fae027d624702c461879bb6be6830b7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "84b38094ae4edd94523ba99a17397243b1784652e39af23d007d22e7fd6d94cc",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-12-12T19:33:26Z",
    "title_canon_sha256": "f1feed4290cdc69744f75e258e45fc03cf4134593a7de386c9816fb4d6b743bf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.2666",
    "kind": "arxiv",
    "version": 2
  }
}