Pith Number

pith:GD7RAX7K

pith:2026:GD7RAX7K32RTUMOUTAPWUBS42Z

not attested not anchored not stored refs resolved

Lefschetz Fibrations on Knot Traces of Alternating and Extended Alternating Knots

Atsushi Tanaka

Knot traces of alternating and extended alternating knots admit positive allowable Lefschetz fibrations whose regular fibers have genus equal to the number of white regions in the associated planar graph.

arxiv:2605.13017 v1 · 2026-05-13 · math.GT

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\pithnumber{GD7RAX7K32RTUMOUTAPWUBS42Z}

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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.

Claims

C1strongest claim

Each such knot trace admits a PALF whose regular fiber has a genus exactly equal to the number of white regions in the associated planar graph.

C2weakest assumption

The prior construction method from the authors' previous work applies without additional obstructions to the 2-handlebody decompositions of these specific knot traces.

C3one line summary

Knot traces of alternating knots and the newly defined extended alternating knots admit PALFs whose regular fibers have genus equal to the number of white regions in their planar graphs.

References

24 extracted · 24 resolved · 0 Pith anchors

[1] Firat , TITLE = 2012 · doi:10.1142/s0219199712500356

[2] Akbulut, Selman and Ozbagci, Burak , TITLE =. Geom. Topol. , FJOURNAL =. 2001 , PAGES =. doi:10.2140/gt.2001.5.319 , URL = 2001 · doi:10.2140/gt.2001.5.319

[3] Akbulut, Selman and Yasui, Kouichi , TITLE =. J. G\"okova Geom. Topol. GGT , FJOURNAL =. 2008 , PAGES = 2008

[4] Adams, Colin C. , TITLE =. 2004 , PAGES = 2004

[5] Avdek, Russell , TITLE =. Algebr. Geom. Topol. , FJOURNAL =. 2013 , NUMBER =. doi:10.2140/agt.2013.13.1613 , URL = 2013 · doi:10.2140/agt.2013.13.1613

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T03:09:00.113383Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

30ff105feadea33a31d4981f6a065cd660290f8ff6d2cf7e87795489d6074b2d

Aliases

arxiv: 2605.13017 · arxiv_version: 2605.13017v1 · doi: 10.48550/arxiv.2605.13017 · pith_short_12: GD7RAX7K32RT · pith_short_16: GD7RAX7K32RTUMOU · pith_short_8: GD7RAX7K

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/GD7RAX7K32RTUMOUTAPWUBS42Z \
  | 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: 30ff105feadea33a31d4981f6a065cd660290f8ff6d2cf7e87795489d6074b2d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e841a77e32ee6491764f72584b3b4bd67df857b877e5e7f39b39d19f2179e242",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2026-05-13T05:15:24Z",
    "title_canon_sha256": "a38408832cdee9f3a8cd5594c69d7f5bffdc6a036a38db656d5b6d6db359ddfe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13017",
    "kind": "arxiv",
    "version": 1
  }
}