Pith Number

pith:Z2BB7LA7

pith:2025:Z2BB7LA774HPG4OE27JIAP7INN

not attested not anchored not stored refs pending

Determining evolutionary equations from a single passive boundary observation

Catharine W. K. Lo, Hongyu Liu, Longyue Tao, Lu Chen, Yan Jiang

A single passive boundary observation can uniquely recover both sources and coefficients in evolutionary PDEs.

arxiv:2505.08473 v7 · 2025-05-13 · math.AP

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\usepackage{pith}
\pithnumber{Z2BB7LA774HPG4OE27JIAP7INN}

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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

This approach yields the first systematic resolution for second-order hyperbolic, parabolic, and Schrödinger equations under a single coherent method. Our unique identifiability results subsume all existing literature and cover more general configurations of practical interest.

C2weakest assumption

The key condition that the measurement dataset's cardinality must exceed the unknowns' by at least one dimension is sufficient to decouple the unknowns and linearize the nonlinear inverse problem, as stated in the abstract as the enabling premise for the framework.

C3one line summary

Establishes unique identifiability for simultaneous recovery of sources and coefficients in second-order hyperbolic, parabolic, and Schrödinger equations from single passive boundary data when the number of measurements exceeds the number of unknowns by at least one dimension.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-26T02:03:50.477126Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ce821fac1fff0ef371c4d7d2803fe86b6d12384a7fca45dcf726a1844178c11d

Aliases

arxiv: 2505.08473 · arxiv_version: 2505.08473v7 · doi: 10.48550/arxiv.2505.08473 · pith_short_12: Z2BB7LA774HP · pith_short_16: Z2BB7LA774HPG4OE · pith_short_8: Z2BB7LA7

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/Z2BB7LA774HPG4OE27JIAP7INN \
  | 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: ce821fac1fff0ef371c4d7d2803fe86b6d12384a7fca45dcf726a1844178c11d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8c4209eeeb09c8087edfcbbd85f137588f45e1bf65efd8bb9eae5cd837d26fb1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-05-13T11:57:28Z",
    "title_canon_sha256": "84f1444bc0e652a2ad1a773b79f82d22ed644ad9f9fb4558417c5526a06232de"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2505.08473",
    "kind": "arxiv",
    "version": 7
  }
}