Pith Number

pith:QP63XPXW

pith:2011:QP63XPXWRIY3SZ6DFYUMDX4ZKY

not attested not anchored not stored refs pending

L2 dimensions of spaces of braid-invariant harmonic forms

Alexander Kalyuzhnyi, Alexei Daletskii

arxiv:1110.4878 v1 · 2011-10-21 · math.FA · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QP63XPXWRIY3SZ6DFYUMDX4ZKY}

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	2026-05-18T02:00:07.090810Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

83fdbbbef68a31b967c32e28c1df99563f0d41fa8db6be8b2513aa1dcf0d4047

Aliases

arxiv: 1110.4878 · arxiv_version: 1110.4878v1 · doi: 10.48550/arxiv.1110.4878 · pith_short_12: QP63XPXWRIY3 · pith_short_16: QP63XPXWRIY3SZ6D · pith_short_8: QP63XPXW

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/QP63XPXWRIY3SZ6DFYUMDX4ZKY \
  | 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: 83fdbbbef68a31b967c32e28c1df99563f0d41fa8db6be8b2513aa1dcf0d4047

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "67297a89683634d970514bacaa39add96363533d913ff7c336f9f6d2e21fa9b1",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-10-21T19:33:38Z",
    "title_canon_sha256": "03eacbd0577f17d8c5610ebb3e93f7b31e98032b64e0e48972fd9e366e545b7a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.4878",
    "kind": "arxiv",
    "version": 1
  }
}