Pith Number

pith:ZYXM5XWB

pith:2023:ZYXM5XWBLJFMXDMCQYHA5L2WJN

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Generalized Brieskorn Modules I: Convergent (a,b)-modules

Daniel Barlet (IUF, IECL), UL

Generalized Brieskorn modules receive a full description through convergent asymptotic expansions of Nilsson class.

arxiv:2307.04395 v3 · 2023-07-10 · math.AG · math.CV

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\pithnumber{ZYXM5XWBLJFMXDMCQYHA5L2WJN}

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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 obtain a full description of generalized Brieskorn-modules in terms of (convergent) asymptotics expansions of Nilsson class which will be used as a starting point in part II.

C2weakest assumption

The formal completion in f of the Brieskorn module does not give access to the cohomology of the Milnor fiber of f, which by definition is outside the zero set of f; this necessitates the introduction of generalized Brieskorn modules.

C3one line summary

Develops the theory of convergent generalized Brieskorn modules, including semi-simple filtration, with a full description via convergent asymptotic expansions of Nilsson class and explicit relation to the nilpotent filtration of monodromy.

Receipt and verification

First computed	2026-05-27T01:05:31.880736Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ce2ecedec15a4acb8d82860e0eaf564b7bf8026a0e68349ef0f5b82b3653597c

Aliases

arxiv: 2307.04395 · arxiv_version: 2307.04395v3 · doi: 10.48550/arxiv.2307.04395 · pith_short_12: ZYXM5XWBLJFM · pith_short_16: ZYXM5XWBLJFMXDMC · pith_short_8: ZYXM5XWB

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/ZYXM5XWBLJFMXDMCQYHA5L2WJN \
  | 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: ce2ecedec15a4acb8d82860e0eaf564b7bf8026a0e68349ef0f5b82b3653597c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "440a13fb969e85e3640dae1016c996909550b5118e37c01407c8b8767a57aca7",
    "cross_cats_sorted": [
      "math.CV"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2023-07-10T07:57:24Z",
    "title_canon_sha256": "150b4e99ddd47326421514a255e84d983c3a38ba4cb736fe495bdec27e7b6b32"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2307.04395",
    "kind": "arxiv",
    "version": 3
  }
}