Pith Number

pith:335MWWO5

pith:2025:335MWWO5U3KNZTDTMDIKTC7QIP

not attested not anchored not stored refs pending

Congruence Subgroups of the Virtual Braid Group

Alexa Goldberg, Nancy Scherich, Wade Bloomquist

arxiv:2510.21593 v2 · 2025-10-24 · 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{335MWWO5U3KNZTDTMDIKTC7QIP}

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	2026-06-09T02:08:34.276096Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

defacb59dda6d4dccc7360d0a98bf043dd40c84ff84fd5ac0aae7bfdd3db1452

Aliases

arxiv: 2510.21593 · arxiv_version: 2510.21593v2 · doi: 10.48550/arxiv.2510.21593 · pith_short_12: 335MWWO5U3KN · pith_short_16: 335MWWO5U3KNZTDT · pith_short_8: 335MWWO5

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/335MWWO5U3KNZTDTMDIKTC7QIP \
  | 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: defacb59dda6d4dccc7360d0a98bf043dd40c84ff84fd5ac0aae7bfdd3db1452

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "35dc1363e7e7d9dec179824edcefb463678298c9bcfa725e284d9fb96a4f5e3d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2025-10-24T16:00:46Z",
    "title_canon_sha256": "fabb27e7c06facacc92768d0549abc0e18c25ce8a5352641bfde55fa38ad29de"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2510.21593",
    "kind": "arxiv",
    "version": 2
  }
}