Pith Number

pith:3TBTA2AW

pith:2026:3TBTA2AWD3BDYJ64CZVYTWO4UE

not attested not anchored not stored refs pending

The Pandharipande-Thomas rationality conjecture for superpositive curve classes on projective complex 3-manifolds

Dominic Joyce, Reginald Anderson

Pandharipande-Thomas invariants have rational generating functions for superpositive curve classes on 3-manifolds

arxiv:2604.05664 v2 · 2026-04-07 · math.AG

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\pithnumber{3TBTA2AWD3BDYJ64CZVYTWO4UE}

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Record completeness

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3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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

We use this theory to prove conjectures by Pandharipande and Thomas on the rationality and poles of generating functions of Pandharipande-Thomas invariants of X with descendent insertions, for superpositive curve classes.

C2weakest assumption

That the enumerative invariants and wall-crossing formulae developed in arXiv:2111.04694 apply without additional obstructions to the superpositive curve classes on any projective complex 3-manifold.

C3one line summary

Proves that generating functions of Pandharipande-Thomas invariants with descendent insertions are rational with controlled poles for superpositive curve classes on projective complex 3-manifolds.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-06-19T16:09:57.930645Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dcc33068161ec23c27dc166b89d9dca116c07f6632b0cb554c37f792d8c69261

Aliases

arxiv: 2604.05664 · arxiv_version: 2604.05664v2 · doi: 10.48550/arxiv.2604.05664 · pith_short_12: 3TBTA2AWD3BD · pith_short_16: 3TBTA2AWD3BDYJ64 · pith_short_8: 3TBTA2AW

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/3TBTA2AWD3BDYJ64CZVYTWO4UE \
  | 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: dcc33068161ec23c27dc166b89d9dca116c07f6632b0cb554c37f792d8c69261

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6aeb190aa81a8e70678a56986aa92f1ac68eb6eec580c260de5775c8a4228dbe",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-04-07T10:05:56Z",
    "title_canon_sha256": "a13a66c0de07833a3f67d0111e83aae18f2d41ac0fa878ab567ac6434630926b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.05664",
    "kind": "arxiv",
    "version": 2
  }
}