Pith Number

pith:X5UKJJSF

pith:2010:X5UKJJSFH4GWJR6MRQ7REEN2XO

not attested not anchored not stored refs pending

Higher-order signature cocycles for subgroups of mapping class groups and homology cylinders

Peter Horn (Columbia University), Shelly Harvey (Rice University), Tim D. Cochran (Rice University)

arxiv:1003.4977 v3 · 2010-03-25 · 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{X5UKJJSFH4GWJR6MRQ7REEN2XO}

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	2026-05-18T02:24:26.627633Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bf68a4a6453f0d64c7cc8c3f1211babb9005c753d9d2279a41795720b275c678

Aliases

arxiv: 1003.4977 · arxiv_version: 1003.4977v3 · doi: 10.48550/arxiv.1003.4977 · pith_short_12: X5UKJJSFH4GW · pith_short_16: X5UKJJSFH4GWJR6M · pith_short_8: X5UKJJSF

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/X5UKJJSFH4GWJR6MRQ7REEN2XO \
  | 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: bf68a4a6453f0d64c7cc8c3f1211babb9005c753d9d2279a41795720b275c678

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "adbbbcc1f4089fe4910ec8479e7103e84b206960beb7183139c5c466d9c08715",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2010-03-25T19:12:59Z",
    "title_canon_sha256": "d663f3dbf9c47bc1894d1f2f4f8ebf87f5314514e70818a95b1d563eefdfee3c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1003.4977",
    "kind": "arxiv",
    "version": 3
  }
}