Pith Number

pith:BTNUL3ES

pith:2021:BTNUL3ESBYVK4OQTWHGZZA6TMJ

not attested not anchored not stored refs pending

Scattering by finely-layered obstacles: frequency-explicit bounds and homogenization

Euan A. Spence, Th\'eophile Chaumont-Frelet

arxiv:2109.11267 v2 · 2021-09-23 · 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{BTNUL3ESBYVK4OQTWHGZZA6TMJ}

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	2026-07-05T04:58:14.438853Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0cdb45ec920e2aae3a13b1cd9c83d36279fed10617f8327f895280c0613ebe2c

Aliases

arxiv: 2109.11267 · arxiv_version: 2109.11267v2 · doi: 10.48550/arxiv.2109.11267 · pith_short_12: BTNUL3ESBYVK · pith_short_16: BTNUL3ESBYVK4OQT · pith_short_8: BTNUL3ES

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/BTNUL3ESBYVK4OQTWHGZZA6TMJ \
  | 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: 0cdb45ec920e2aae3a13b1cd9c83d36279fed10617f8327f895280c0613ebe2c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ca1cff2b8f9f2e70cc43aca292a2f994202813281c796efe0d732efab80534d7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2021-09-23T10:12:14Z",
    "title_canon_sha256": "04cb34ef914f6a30214fd40dcd9627811beeb136e51c8269944439eed1a355d2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2109.11267",
    "kind": "arxiv",
    "version": 2
  }
}