Pith Number

pith:65R5QXPM

pith:2016:65R5QXPM4I47KRY2HEK7YXNUSJ

not attested not anchored not stored refs pending

How efficiently can one untangle a double-twist? Waving is believing!

Daniel Ramras, David Pengelley

arxiv:1610.04680 v2 · 2016-10-15 · math.GT · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{65R5QXPM4I47KRY2HEK7YXNUSJ}

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	2026-05-18T00:16:39.097583Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f763d85dece239f5471a3915fc5db492615cf3e3ff827f3e696d4b61b77c89d5

Aliases

arxiv: 1610.04680 · arxiv_version: 1610.04680v2 · doi: 10.48550/arxiv.1610.04680 · pith_short_12: 65R5QXPM4I47 · pith_short_16: 65R5QXPM4I47KRY2 · pith_short_8: 65R5QXPM

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/65R5QXPM4I47KRY2HEK7YXNUSJ \
  | 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: f763d85dece239f5471a3915fc5db492615cf3e3ff827f3e696d4b61b77c89d5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f5bcae45cc9484499c64316a348af4439a458554403cbe93e8cc6f0f608d312e",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2016-10-15T01:48:02Z",
    "title_canon_sha256": "4838bd95e39ac1dabf7150ccbce12baf424047dc8546b8eb40073f472f06a494"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.04680",
    "kind": "arxiv",
    "version": 2
  }
}