Pith Number

pith:HFY2LSFQ

pith:2026:HFY2LSFQVCU6VR2YPS32HCOVK5

not attested not anchored not stored refs pending

Mesh-Intrinsic GFEM: Asymptotic Smoothness on C^0 Unstructured Meshes

Rong Tian

Local polynomial reconstructions on overlapping patches blended by partition of unity cancel derivative jumps exactly for polynomials on standard C0 meshes.

arxiv:2604.23155 v2 · 2026-04-25 · math.NA · cs.NA

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\pithnumber{HFY2LSFQVCU6VR2YPS32HCOVK5}

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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

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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 core analysis establishes a partition-of-zero (PoZ) smoothness-transfer mechanism driven by interface coherence: derivative jumps cancel exactly for polynomial reproduction and decay as O(h^{p+1-||α||}) for smooth nonpolynomial fields.

C2weakest assumption

That local polynomial reconstructions on overlapping nodal patches, when blended by partition of unity, produce interface coherence sufficient for exact derivative-jump cancellation on polynomials and the stated decay rate on non-polynomials, without additional global constraints or post-processing.

C3one line summary

MiGFEM introduces a partition-of-zero smoothness-transfer mechanism that cancels derivative jumps exactly for polynomials and decays appropriately for smooth fields, enabling polynomial-exact intrinsic derivatives on C0 meshes.

Receipt and verification

First computed	2026-06-23T02:13:24.220388Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3971a5c8b0a8a9eac7587cb7a389d55743540fb7c479e5f406e90377e585ded5

Aliases

arxiv: 2604.23155 · arxiv_version: 2604.23155v2 · doi: 10.48550/arxiv.2604.23155 · pith_short_12: HFY2LSFQVCU6 · pith_short_16: HFY2LSFQVCU6VR2Y · pith_short_8: HFY2LSFQ

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/HFY2LSFQVCU6VR2YPS32HCOVK5 \
  | 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: 3971a5c8b0a8a9eac7587cb7a389d55743540fb7c479e5f406e90377e585ded5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a3934d85dfb6686bb9e6dadd7659454b8c821469419c87fb7c2465cd550883ff",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-04-25T05:58:21Z",
    "title_canon_sha256": "1a338c0ea5f4827d8ff1451466ad9161765ff492d89bd178e55edad77ad2a4b9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.23155",
    "kind": "arxiv",
    "version": 2
  }
}