Pith Number

pith:IUMXUMI7

pith:2026:IUMXUMI7JLNDXHCD54ZZSKDOUV

not attested not anchored not stored refs resolved

Nonlocal thermal Willis coupling in laminated conductors

Chunlin Wu, Gal Shmuel, Huiming Yin

Periodic laminates produce consistent nonlocal cross-coupling in their thermal response.

arxiv:2605.16983 v1 · 2026-05-16 · math-ph · math.AP · math.MP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IUMXUMI7JLNDXHCD54ZZSKDOUV}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

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

The three approaches yield consistent nonlocal cross-coupling terms, clarifying the roles of spatial asymmetry and averaging choice. We also calculate the corresponding thermal impedance and show that it is direction-dependent.

C2weakest assumption

The periodic laminate geometry and the three independent homogenization procedures correctly capture spatial nonlocality beyond the subwavelength regime assumed in prior numerical examples (abstract).

C3one line summary

Computes nonlocal effective kernels for thermal bianisotropy in periodic laminates using three homogenization methods, revealing consistent cross-coupling terms and direction-dependent thermal impedance.

References

55 extracted · 55 resolved · 0 Pith anchors

[1] 2013 Metamaterials beyond electromagnetism.Reports on Progress in Physics76, 126501 2013

[2] 2019 3D metamaterials.Nature Reviews Physics1, 198–210 2019 · doi:10.1038/s42254-018-0018-y

[3] 2015 Elastic metamaterials and dynamic homogenization: a review.International Journal of Smart and Nano Materials6, 41–60 2015

[4] 2015 Vibrant times for mechanical metamaterials.MRS Communi- cations5, 453–462 2015 · doi:10.1557/mrc.2015.51

[5] 2013 Experiments on Transformation Thermodynamics: Molding the Flow of Heat.Physical Review Letters110, 195901 2013 · doi:10.1103/physrevlett.110.195901

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:03:34.375116Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

45197a311f4ada3b9c43ef3399286ea544406169a45586c4bfd4686c473b88c8

Aliases

arxiv: 2605.16983 · arxiv_version: 2605.16983v1 · doi: 10.48550/arxiv.2605.16983 · pith_short_12: IUMXUMI7JLND · pith_short_16: IUMXUMI7JLNDXHCD · pith_short_8: IUMXUMI7

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/IUMXUMI7JLNDXHCD54ZZSKDOUV \
  | 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: 45197a311f4ada3b9c43ef3399286ea544406169a45586c4bfd4686c473b88c8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "99285ae7f4ec8322054a88f72ac1349725fa28d4a78b3213285b5be26aa6165f",
    "cross_cats_sorted": [
      "math.AP",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-05-16T13:06:18Z",
    "title_canon_sha256": "429d34befaeb387c65130cdf6d8df28730e9e2d8808183deb1044542e1cc8b7f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16983",
    "kind": "arxiv",
    "version": 1
  }
}