Pith Number

pith:FPFAX3HC

pith:2026:FPFAX3HCB5S526RY7UG4N2V6CL

not attested not anchored not stored refs pending

Brunnian braids and the inclusion from double shuffle Lie algebra to Kashiwara-Vergne Lie algebra

Muze Ren

arxiv:2605.20844 v1 · 2026-05-20 · math.QA · 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{FPFAX3HCB5S526RY7UG4N2V6CL}

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	2026-05-21T01:05:24.251234Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2bca0bece20f65dd7a38fd0dc6eabe12f42360b40f69bdfd57bdc780c640b3d0

Aliases

arxiv: 2605.20844 · arxiv_version: 2605.20844v1 · doi: 10.48550/arxiv.2605.20844 · pith_short_12: FPFAX3HCB5S5 · pith_short_16: FPFAX3HCB5S526RY · pith_short_8: FPFAX3HC

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/FPFAX3HCB5S526RY7UG4N2V6CL \
  | 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: 2bca0bece20f65dd7a38fd0dc6eabe12f42360b40f69bdfd57bdc780c640b3d0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0a62e9a591f7c77bcb161adf7aae1cd24b17ad896a4a2b6e0b5bcd3d1a3449dc",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2026-05-20T07:33:35Z",
    "title_canon_sha256": "14d9e4d33e3c168b0c7ded6ecda6df34892e3af0edf44b680d1e1440e7a395c1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.20844",
    "kind": "arxiv",
    "version": 1
  }
}