Pith Number

pith:F3PB2NBK

pith:2013:F3PB2NBKYNY5ER3FP67C2IBWXJ

not attested not anchored not stored refs pending

Bi-invariant metrics and quasi-morphisms on groups of Hamiltonian diffeomorphisms of surfaces

Michael Brandenbursky

arxiv:1306.3350 v3 · 2013-06-14 · math.GT · math.GR · math.SG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{F3PB2NBKYNY5ER3FP67C2IBWXJ}

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	2026-05-18T02:50:50.572426Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2ede1d342ac371d247657fbe2d2036ba702ab57cac3a42995ce8463591084c78

Aliases

arxiv: 1306.3350 · arxiv_version: 1306.3350v3 · doi: 10.48550/arxiv.1306.3350 · pith_short_12: F3PB2NBKYNY5 · pith_short_16: F3PB2NBKYNY5ER3F · pith_short_8: F3PB2NBK

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/F3PB2NBKYNY5ER3FP67C2IBWXJ \
  | 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: 2ede1d342ac371d247657fbe2d2036ba702ab57cac3a42995ce8463591084c78

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "16077de5df971e88b144591517139471edba3593f2d09e56278e3dc9eb676b8b",
    "cross_cats_sorted": [
      "math.GR",
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2013-06-14T09:48:04Z",
    "title_canon_sha256": "08b1e29b917725bab80edc9660fb2f643784be27e2f416a51c72d86d9c5ea03d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.3350",
    "kind": "arxiv",
    "version": 3
  }
}