Pith Number

pith:I3V6R3NH

pith:2016:I3V6R3NHVF6UZ7KOTMVMGABLXF

not attested not anchored not stored refs pending

Bloch Wave Homogenization Relative to a Microstructure

Muthusamy Vanninathan, Tuhin Ghosh

arxiv:1608.07552 v1 · 2016-08-26 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{I3V6R3NHVF6UZ7KOTMVMGABLXF}

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	2026-05-18T01:07:52.778532Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

46ebe8eda7a97d4cfd4e9b2ac3002bb97e47e102f1d04e143fec59186aa08d5f

Aliases

arxiv: 1608.07552 · arxiv_version: 1608.07552v1 · doi: 10.48550/arxiv.1608.07552 · pith_short_12: I3V6R3NHVF6U · pith_short_16: I3V6R3NHVF6UZ7KO · pith_short_8: I3V6R3NH

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/I3V6R3NHVF6UZ7KOTMVMGABLXF \
  | 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: 46ebe8eda7a97d4cfd4e9b2ac3002bb97e47e102f1d04e143fec59186aa08d5f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "899133bd5facf6338476dbea9304c5a08f84d1655fa55e39ca2cba79fb749eeb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-08-26T18:28:40Z",
    "title_canon_sha256": "6e6872204d6cf76abc2635dddaf28798f7c906503b6d6543ea982242a05ee99e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.07552",
    "kind": "arxiv",
    "version": 1
  }
}