Pith Number

pith:JCS7WSFV

pith:2009:JCS7WSFV2IWZ3EAKER36J7HVBU

not attested not anchored not stored refs pending

Group actions on 4-manifolds: some recent results and open questions

Weimin Chen

arxiv:0912.2662 v2 · 2009-12-14 · math.GT · 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{JCS7WSFV2IWZ3EAKER36J7HVBU}

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	2026-05-18T04:40:56.061351Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

48a5fb48b5d22d9d900a2477e4fcf50d04fc894c95513b5623d1d69b32d9aab0

Aliases

arxiv: 0912.2662 · arxiv_version: 0912.2662v2 · doi: 10.48550/arxiv.0912.2662 · pith_short_12: JCS7WSFV2IWZ · pith_short_16: JCS7WSFV2IWZ3EAK · pith_short_8: JCS7WSFV

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/JCS7WSFV2IWZ3EAKER36J7HVBU \
  | 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: 48a5fb48b5d22d9d900a2477e4fcf50d04fc894c95513b5623d1d69b32d9aab0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2ced65475b5bbfc3d448e166342f5bbff8015b5a925bffa1be9b559fccc2c4e1",
    "cross_cats_sorted": [
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2009-12-14T15:18:25Z",
    "title_canon_sha256": "93d79b21b00febf753eeee20d70e9b5e0cdd484c9ee2697d1ab2be6821286e24"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.2662",
    "kind": "arxiv",
    "version": 2
  }
}