Pith Number

pith:4UHV2RSL

pith:2018:4UHV2RSLZOKT6QZRIFMLEYAZCO

not attested not anchored not stored refs pending

Fragmentation norm and relative quasimorphisms

Jarek K\k{e}dra, Michael Brandenbursky

arxiv:1804.06592 v2 · 2018-04-18 · math.GT · math.DS · 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{4UHV2RSLZOKT6QZRIFMLEYAZCO}

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	2026-05-17T23:47:31.234891Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e50f5d464bcb953f43314158b2601913843390fa47177b41a43e8244afe21caa

Aliases

arxiv: 1804.06592 · arxiv_version: 1804.06592v2 · doi: 10.48550/arxiv.1804.06592 · pith_short_12: 4UHV2RSLZOKT · pith_short_16: 4UHV2RSLZOKT6QZR · pith_short_8: 4UHV2RSL

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/4UHV2RSLZOKT6QZRIFMLEYAZCO \
  | 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: e50f5d464bcb953f43314158b2601913843390fa47177b41a43e8244afe21caa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "99168d4b5afbd14c107243d213b3c4d3d13281621143350e567ecc60e3d794ac",
    "cross_cats_sorted": [
      "math.DS",
      "math.GR",
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2018-04-18T07:52:32Z",
    "title_canon_sha256": "747f06c49cd705f2ac8963148a1198ec98a39f2d74300a967bfdf341d81bb3e7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1804.06592",
    "kind": "arxiv",
    "version": 2
  }
}