Pith Number

pith:NM6UI6M2

pith:2026:NM6UI6M2GPWJFSUXVWSKNSIDJK

not attested not anchored not stored refs pending

On the quasi-monomiality of the $\alpha$- and $\delta$-invariants

Dae-Won Lee, Donghyeon Kim

Quasi-monomial valuations compute the alpha and delta invariants for any projective klt pair with ample line bundle, over countable or uncountable fields.

arxiv:2604.18465 v3 · 2026-04-20 · math.AG

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\pithnumber{NM6UI6M2GPWJFSUXVWSKNSIDJK}

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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

For any projective klt pair (X,Δ) and ample line bundle L, there exist quasi-monomial valuations computing α(X,Δ,L) and δ(X,Δ,L), independently of whether the base field is countable.

C2weakest assumption

The pair (X,Δ) is klt and projective with L ample; the argument likely depends on the existence of suitable models or resolutions that may require additional technical conditions from birational geometry.

C3one line summary

Quasi-monomial valuations exist that compute α(X,Δ,L) and δ(X,Δ,L) for projective klt pairs over arbitrary fields.

Cited by

2 papers in Pith

On the normalized local volume of a non-closed point

Receipt and verification

First computed	2026-05-20T00:05:44.868442Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6b3d44799a33ec92ca97ada4a6c9034ab0848175c8bd50d5da69dfc0d4f331d1

Aliases

arxiv: 2604.18465 · arxiv_version: 2604.18465v3 · doi: 10.48550/arxiv.2604.18465 · pith_short_12: NM6UI6M2GPWJ · pith_short_16: NM6UI6M2GPWJFSUX · pith_short_8: NM6UI6M2

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/NM6UI6M2GPWJFSUXVWSKNSIDJK \
  | 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: 6b3d44799a33ec92ca97ada4a6c9034ab0848175c8bd50d5da69dfc0d4f331d1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "062d1e41d61c862f960fa4861ebc5c87bdde0f9050a8e9dc308ad7eaa3dd888c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-04-20T16:19:16Z",
    "title_canon_sha256": "1474816289ae4eabb824e86d72d84a3f2e6f4701f0806ac66cf69a45afeba228"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.18465",
    "kind": "arxiv",
    "version": 3
  }
}