Pith Number

pith:W65RHE5X

pith:2013:W65RHE5X7CIT2ZP4AEWTZ6YCUA

not attested not anchored not stored refs pending

$G$-minimality and invariant negative spheres in $G$-Hirzebruch surfaces

Weimin Chen

arxiv:1312.0848 v3 · 2013-12-03 · 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{W65RHE5X7CIT2ZP4AEWTZ6YCUA}

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	2026-05-18T01:53:09.628515Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b7bb1393b7f8913d65fc012d3cfb02a009f3b3926bf06fcc6f802476f6f08acc

Aliases

arxiv: 1312.0848 · arxiv_version: 1312.0848v3 · doi: 10.48550/arxiv.1312.0848 · pith_short_12: W65RHE5X7CIT · pith_short_16: W65RHE5X7CIT2ZP4 · pith_short_8: W65RHE5X

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/W65RHE5X7CIT2ZP4AEWTZ6YCUA \
  | 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: b7bb1393b7f8913d65fc012d3cfb02a009f3b3926bf06fcc6f802476f6f08acc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ff57fc6b7e1da91da3184f2d7208b05f4cf453bc47a8799cc8957bd92128e5fe",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2013-12-03T15:19:41Z",
    "title_canon_sha256": "7291da07527764c0270f8b1a7e98ca62ff6008a61753272a8d50238f70da8bb8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.0848",
    "kind": "arxiv",
    "version": 3
  }
}