Pith Number

pith:WMNYAFAR

pith:2026:WMNYAFARE3B7O6PM7GSLEBJEHL

not attested not anchored not stored refs resolved

Exponential concentration for quantum periods via mirror symmetry

Hua-Zhong Ke, Jianxun Hu, Jingwei Lu

Quantum periods of Fano manifolds satisfy the exponential concentration property when they admit convenient weak Landau-Ginzburg models with non-negative coefficients.

arxiv:2605.16051 v1 · 2026-05-15 · math.AG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WMNYAFARE3B7O6PM7GSLEBJEHL}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

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

we prove that the quantum period of a Fano manifold possesses the same property, whenever the manifold admits a convenient weak Landau-Ginzburg model with non-negative coefficients.

C2weakest assumption

The Fano manifold admits a convenient weak Landau-Ginzburg model with non-negative coefficients (extracted from the abstract statement of the geometric application).

C3one line summary

Modified hypergeometric series respect the exponential concentration property, implying the same for quantum periods of Fano manifolds admitting convenient weak Landau-Ginzburg models with non-negative coefficients.

References

13 extracted · 13 resolved · 3 Pith anchors

[1] Gamma conjecture I for flag varieties 2013 · arXiv:2501.13221

[2] Databases of quantum periods for Fano manifolds 2022

[3] The conifold point 2011 · arXiv:1404.7388

[4] On the quantum product of Schubert classes 2016

[5] Adv. Stud. Pure Math. Tokyo: Mathematical Society of Japan, 2019, pp. 55– 2019

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:01:50.728205Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b31b80141126c3f779ecf9a4b205243afb5045944c470f711c4ee7dba31627b1

Aliases

arxiv: 2605.16051 · arxiv_version: 2605.16051v1 · doi: 10.48550/arxiv.2605.16051 · pith_short_12: WMNYAFARE3B7 · pith_short_16: WMNYAFARE3B7O6PM · pith_short_8: WMNYAFAR

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/WMNYAFARE3B7O6PM7GSLEBJEHL \
  | 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: b31b80141126c3f779ecf9a4b205243afb5045944c470f711c4ee7dba31627b1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "20f48d0c57c412a40207e3a593736c1b21ef814e4c5f520e086c9a4dc2aee9b0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-05-15T15:19:10Z",
    "title_canon_sha256": "e0482a9fb0f08369d491ff84e1e591fc13cd6e7a57a5086c3507610359521323"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16051",
    "kind": "arxiv",
    "version": 1
  }
}