Pith Number

pith:XZKG7Z4V

pith:2013:XZKG7Z4VCHUZVIGPG6626HLJFO

not attested not anchored not stored refs pending

Unimodality of the Betti numbers for Hamiltonian circle action with isolated fixed points

Min Kyu Kim, Yunhyung Cho

arxiv:1309.1322 v1 · 2013-09-05 · 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{XZKG7Z4VCHUZVIGPG6626HLJFO}

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	2026-05-18T03:14:07.590643Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

be546fe79511e99aa0cf37bdaf1d692bb7a64f80d4fd47ddb1ebfe188d346c4b

Aliases

arxiv: 1309.1322 · arxiv_version: 1309.1322v1 · doi: 10.48550/arxiv.1309.1322 · pith_short_12: XZKG7Z4VCHUZ · pith_short_16: XZKG7Z4VCHUZVIGP · pith_short_8: XZKG7Z4V

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/XZKG7Z4VCHUZVIGPG6626HLJFO \
  | 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: be546fe79511e99aa0cf37bdaf1d692bb7a64f80d4fd47ddb1ebfe188d346c4b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d428c9154e96a3ef5d287fcc88fbe0970ec1c09e33d0020edd7ba5a01c75e043",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2013-09-05T11:52:17Z",
    "title_canon_sha256": "77044c15ecb1b1945127f4e4670f0b32d8a0046d8a9d20f1795fd15a4726fa01"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.1322",
    "kind": "arxiv",
    "version": 1
  }
}