Pith Number

pith:DUYW7S6T

pith:2025:DUYW7S6THGN24KJFJ6Z3M6X6ME

not attested not anchored not stored refs pending

Kolmogorov equations for evaluating the boundary hitting of degenerate diffusion with unsteady drift

Hidekazu Yoshioka

The finite difference method for linear and nonlinear Kolmogorov equations of unsteady Jacobi diffusion yields unique numerical solutions due to discrete ellipticity when the discount is positive.

arxiv:2501.02729 v5 · 2025-01-06 · math.NA · cs.NA

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\pithnumber{DUYW7S6THGN24KJFJ6Z3M6X6ME}

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Record completeness

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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

The finite difference method for the linear and nonlinear Kolmogorov equations yields a unique numerical solution because of discrete ellipticity if the discount is positive.

C2weakest assumption

The accuracy of the finite difference method critically depends on the regularity of the boundary condition, and the use of high-order discretization is not always effective.

C3one line summary

Develops Kolmogorov equations and finite difference methods for boundary hitting in degenerate Jacobi diffusions with unsteady drift, with a mean-field tourism application.

Receipt and verification

First computed	2026-06-03T01:05:03.935692Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1d316fcbd3399bae29254fb3b67afe6130c553282f491775c5bcdfe6c2bf3ca2

Aliases

arxiv: 2501.02729 · arxiv_version: 2501.02729v5 · doi: 10.48550/arxiv.2501.02729 · pith_short_12: DUYW7S6THGN2 · pith_short_16: DUYW7S6THGN24KJF · pith_short_8: DUYW7S6T

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/DUYW7S6THGN24KJFJ6Z3M6X6ME \
  | 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: 1d316fcbd3399bae29254fb3b67afe6130c553282f491775c5bcdfe6c2bf3ca2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2e0d24dcecb294a6e02fd3261674dcc255a62d221f03ca7306f8ebfa44db7196",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2025-01-06T02:57:44Z",
    "title_canon_sha256": "1595eec001b9f6932ebb2e9f69cee5f6055215d70c651b2976ff86106c297db4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2501.02729",
    "kind": "arxiv",
    "version": 5
  }
}