Pith Number

pith:OL4AF6B5

pith:2001:OL4AF6B53AYR4VQZHS5X7VO6ZC

not attested not anchored not stored refs pending

Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and Gromov - Witten invariants

Boris Dubrovin, Youjin Zhang

arxiv:math/0108160 v1 · 2001-08-23 · math.DG · math-ph · math.MP · nlin.SI

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OL4AF6B53AYR4VQZHS5X7VO6ZC}

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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

4 papers in Pith

Elliptic orbifold lines and integrable hierarchies

Beyond descendants: integrable observables for cohomological field theories

Universal formulae for correlators of a broad class of models

Generalised (bi-)Hamiltonian structures of hydrodynamic type and (bi-)flat F-manifolds

Receipt and verification

First computed	2026-07-04T14:35:29.406287Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

72f802f83dd8311e56193cbb7fd5dec89038d1a7f8ea4f7486f326cea13e35d2

Aliases

arxiv: math/0108160 · arxiv_version: math/0108160v1 · doi: 10.48550/arxiv.math/0108160 · pith_short_12: OL4AF6B53AYR · pith_short_16: OL4AF6B53AYR4VQZ · pith_short_8: OL4AF6B5

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/OL4AF6B53AYR4VQZHS5X7VO6ZC \
  | 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: 72f802f83dd8311e56193cbb7fd5dec89038d1a7f8ea4f7486f326cea13e35d2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6953c491db6ce351a792fe8cab5481586a09dc4df9b84e3e17b9c6a9eaa5eb05",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "nlin.SI"
    ],
    "license": "",
    "primary_cat": "math.DG",
    "submitted_at": "2001-08-23T13:57:44Z",
    "title_canon_sha256": "0d9186508566dd1267b6700cb72b42f45f9e6b0120ba41bd70e32ff215775363"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0108160",
    "kind": "arxiv",
    "version": 1
  }
}