Pith Number

pith:657WKZK5

pith:2015:657WKZK5LZAATUKZHLRT4BOK2I

not attested not anchored not stored refs pending

The fundamental group of symplectic $4$-manifolds with $b^+=1$

Anar Akhmedov, Weiyi Zhang

arxiv:1506.08367 v2 · 2015-06-28 · math.GT · math.AG · 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{657WKZK5LZAATUKZHLRT4BOK2I}

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	2026-05-18T01:33:51.416574Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f77f65655d5e4009d1593ae33e05cad235f00e7f29f4ed45eb0c7a5d90bac373

Aliases

arxiv: 1506.08367 · arxiv_version: 1506.08367v2 · doi: 10.48550/arxiv.1506.08367 · pith_short_12: 657WKZK5LZAA · pith_short_16: 657WKZK5LZAATUKZ · pith_short_8: 657WKZK5

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/657WKZK5LZAATUKZHLRT4BOK2I \
  | 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: f77f65655d5e4009d1593ae33e05cad235f00e7f29f4ed45eb0c7a5d90bac373

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c46654c254a7989f55be3da6e85b1d2cf67069e0ed7da0cebc2faf7b41614035",
    "cross_cats_sorted": [
      "math.AG",
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2015-06-28T07:05:42Z",
    "title_canon_sha256": "76bc19175184b25f2a1c6e59acc8e3ccac9bf88bb75bf1ac1fe13459529c19d1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.08367",
    "kind": "arxiv",
    "version": 2
  }
}