Pith Number

pith:QA35SOQU

pith:2016:QA35SOQUDVOTPSRYFXN3D7TEJ6

not attested not anchored not stored refs pending

On upper and lower bounds for finite group actions on bounded surfaces, handlebodies, closed handles and finite graphs

Bruno P. Zimmermann

arxiv:1604.06695 v1 · 2016-04-22 · 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{QA35SOQUDVOTPSRYFXN3D7TEJ6}

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	2026-05-18T01:16:28.397951Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8037d93a141d5d37ca382ddbb1fe644fbdf5aff13abeafa2a5dd245668055255

Aliases

arxiv: 1604.06695 · arxiv_version: 1604.06695v1 · doi: 10.48550/arxiv.1604.06695 · pith_short_12: QA35SOQUDVOT · pith_short_16: QA35SOQUDVOTPSRY · pith_short_8: QA35SOQU

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/QA35SOQUDVOTPSRYFXN3D7TEJ6 \
  | 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: 8037d93a141d5d37ca382ddbb1fe644fbdf5aff13abeafa2a5dd245668055255

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "74ac67a8dbc22a04498cb987b4b450290ba57142a9a9f0d4a730726110750958",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2016-04-22T15:00:48Z",
    "title_canon_sha256": "9fc20ba39262ef5fbe37bc2a25f491314526b567bbdaf20926c3cdfc455d3d17"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1604.06695",
    "kind": "arxiv",
    "version": 1
  }
}