Pith Number

pith:NGMKFM2K

pith:2024:NGMKFM2KZXEA5KHKWQLT7A5TM3

not attested not anchored not stored refs pending

On a classification of Morse functions on $3$-dimensional manifolds represented as connected sums of manifolds of Heegaard genus one

Naoki Kitazawa

arxiv:2411.15943 v2 · 2024-11-24 · math.GT · math.AT

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NGMKFM2KZXEA5KHKWQLT7A5TM3}

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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.

Cited by

1 paper in Pith

Morse functions with regular level sets consisting of $2$-dimensional spheres, $2$-dimensional tori, or Klein Bottles

Receipt and verification

First computed	2026-07-05T09:41:04.418527Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6998a2b34acdc80ea8eab4173f83b366d1a27b673b1932c8b45242c7b020af10

Aliases

arxiv: 2411.15943 · arxiv_version: 2411.15943v2 · doi: 10.48550/arxiv.2411.15943 · pith_short_12: NGMKFM2KZXEA · pith_short_16: NGMKFM2KZXEA5KHK · pith_short_8: NGMKFM2K

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/NGMKFM2KZXEA5KHKWQLT7A5TM3 \
  | 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: 6998a2b34acdc80ea8eab4173f83b366d1a27b673b1932c8b45242c7b020af10

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2523b521163e9eec1100c36e4ab5a66e176f182d2f4fbdf5324aaac87922a4ea",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2024-11-24T18:10:20Z",
    "title_canon_sha256": "96f1643f129879277a0b79f082298aa99760b689ddf27e5cccb43c832a4933f0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2411.15943",
    "kind": "arxiv",
    "version": 2
  }
}