Pith Number

pith:RHQWKGBN

pith:2015:RHQWKGBNSWPAHJUBIZDOYKDFT4

not attested not anchored not stored refs pending

Thurston's Operations on the Braid Groups

Viktor Lopatkin

arxiv:1509.01834 v2 · 2015-09-06 · math.AT · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{RHQWKGBNSWPAHJUBIZDOYKDFT4}

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	2026-05-18T01:33:23.742307Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

89e165182d959e03a6814646ec28659f3b04b89f8055cc0e87e27021cf5a429c

Aliases

arxiv: 1509.01834 · arxiv_version: 1509.01834v2 · doi: 10.48550/arxiv.1509.01834 · pith_short_12: RHQWKGBNSWPA · pith_short_16: RHQWKGBNSWPAHJUB · pith_short_8: RHQWKGBN

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/RHQWKGBNSWPAHJUBIZDOYKDFT4 \
  | 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: 89e165182d959e03a6814646ec28659f3b04b89f8055cc0e87e27021cf5a429c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "68fdebe6a998df050e2865da5f0a77151b6ba4b2c4d25441ae6901e314326664",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2015-09-06T17:16:14Z",
    "title_canon_sha256": "6f2898888f2ee633e695d503b4a0383b3af2dd84ad0c68c93a339ebea88bad20"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.01834",
    "kind": "arxiv",
    "version": 2
  }
}