Pith Number

pith:PT3LQO6L

pith:2026:PT3LQO6LK7W6YYML23R5SMN7GP

not attested not anchored not stored refs pending

Reentrant value fields as delayed coupled reaction-diffusion systems on finite graphs

Karsten Bohlen

Reentrant value fields on finite graphs form well-posed delayed reaction-diffusion systems that admit compact global attractors and delay-independent stability of principal components.

arxiv:2605.03940 v3 · 2026-05-05 · math.DS

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Record completeness

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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

The main formal results are: (1) well-posedness of the full deterministic RFDE under constant input u*, (2) existence of a compact global attractor from compact viability and eventual compactness of solution segments, (3) delay-independent global stability of the principal components (H_L, X_R, P) in the closed stability regime with fixed interfield coupling operators satisfying C_K^2 < μ_L μ_R, (4) SE(d)-invariance of the scalar geometric feature dynamics, and (5) an O(1/κ_Y) fast relaxation estimate for the valuative variable.

C2weakest assumption

Joint non-emptiness of all admissible classes is assumed.

C3one line summary

Establishes well-posedness, compact global attractors, and delay-independent global stability for retarded functional differential equations modeling reentrant value fields as coupled reaction-diffusion systems on finite graphs.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-21T02:05:03.920652Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7cf6b83bcb57edec618bd6e3d931bf33e3308519cdb6e84e0b859a53a065b617

Aliases

arxiv: 2605.03940 · arxiv_version: 2605.03940v3 · doi: 10.48550/arxiv.2605.03940 · pith_short_12: PT3LQO6LK7W6 · pith_short_16: PT3LQO6LK7W6YYML · pith_short_8: PT3LQO6L

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/PT3LQO6LK7W6YYML23R5SMN7GP \
  | 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: 7cf6b83bcb57edec618bd6e3d931bf33e3308519cdb6e84e0b859a53a065b617

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "57a136e454ba010e99b518cc8219b9637bdea007f0a0497e4afd749d7d2462ce",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-05-05T16:29:44Z",
    "title_canon_sha256": "a9431e620387bae65c9d55acb4f06b18ef597f37509519c143c8fff46833201f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.03940",
    "kind": "arxiv",
    "version": 3
  }
}