Pith Number

pith:VXOFAFFF

pith:2024:VXOFAFFFY7EC6ENOTPECJBOG4G

not attested not anchored not stored refs pending

Characterizing $3$-dimensional manifolds represented as connected sums of Lens spaces, $S^2 \times S^1$, and torus bundles over the circle by certain Morse-Bott functions

Naoki Kitazawa

arxiv:2412.11397 v2 · 2024-12-16 · 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{VXOFAFFFY7EC6ENOTPECJBOG4G}

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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	2026-07-05T09:53:08.962900Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

addc5014a5c7c82f11ae9bc82485c6e19dcaecf428fe2c669bbedd83397782b8

Aliases

arxiv: 2412.11397 · arxiv_version: 2412.11397v2 · doi: 10.48550/arxiv.2412.11397 · pith_short_12: VXOFAFFFY7EC · pith_short_16: VXOFAFFFY7EC6ENO · pith_short_8: VXOFAFFF

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/VXOFAFFFY7EC6ENOTPECJBOG4G \
  | 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: addc5014a5c7c82f11ae9bc82485c6e19dcaecf428fe2c669bbedd83397782b8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "38fc285f5ad0392e65d849451294ebce04d57ffe6d22e09aa436c658bc8b5d8f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2024-12-16T02:52:53Z",
    "title_canon_sha256": "5630d1cbbdc91e74d1d20dd6e6d19f291ccfdb62fd45baf260ad239508b61c71"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.11397",
    "kind": "arxiv",
    "version": 2
  }
}