Pith Number

pith:SJFMZH3Z

pith:2010:SJFMZH3ZZQA7RY6BLVOAMP4GEM

not attested not anchored not stored refs pending

Minimum variational principles for time-harmonic waves in a dissipative medium and associated variational principles of Hashin--Shtrikman type

Graeme W. Milton, John R. Willis

arxiv:1001.2773 v1 · 2010-01-15 · math-ph · 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{SJFMZH3ZZQA7RY6BLVOAMP4GEM}

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.

Receipt and verification

First computed	2026-05-18T02:09:43.552617Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

924acc9f79cc01f8e3c15d5c063f8623375ae8306aace7ccb5362fb13aaa0ffa

Aliases

arxiv: 1001.2773 · arxiv_version: 1001.2773v1 · doi: 10.48550/arxiv.1001.2773 · pith_short_12: SJFMZH3ZZQA7 · pith_short_16: SJFMZH3ZZQA7RY6B · pith_short_8: SJFMZH3Z

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/SJFMZH3ZZQA7RY6BLVOAMP4GEM \
  | 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: 924acc9f79cc01f8e3c15d5c063f8623375ae8306aace7ccb5362fb13aaa0ffa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f13ec1a7c6358f50ea12dcc229e0e477e70f92644484ecf4ed36858666978d5e",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2010-01-15T21:06:42Z",
    "title_canon_sha256": "b281b847458a6d72525e3493dcaef31055104c86797ca0c2477ea113a66bf824"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1001.2773",
    "kind": "arxiv",
    "version": 1
  }
}