Pith Number

pith:XQ56LPDU

pith:2011:XQ56LPDU5NAJIISNBZL6XBQLID

not attested not anchored not stored refs pending

Asymptotic Expansion for Multiscale Problems on Non-periodic Stochastic Geometries

Martin Heida

arxiv:1101.4090 v1 · 2011-01-21 · 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{XQ56LPDU5NAJIISNBZL6XBQLID}

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	2026-05-18T02:22:50.806731Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bc3be5bc74eb4094224d0e57eb860b40e9a4b6bf1b98b5caabe1bb1132d1206c

Aliases

arxiv: 1101.4090 · arxiv_version: 1101.4090v1 · doi: 10.48550/arxiv.1101.4090 · pith_short_12: XQ56LPDU5NAJ · pith_short_16: XQ56LPDU5NAJIISN · pith_short_8: XQ56LPDU

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/XQ56LPDU5NAJIISNBZL6XBQLID \
  | 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: bc3be5bc74eb4094224d0e57eb860b40e9a4b6bf1b98b5caabe1bb1132d1206c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0ad9a423b5cec5378387c8972bfe66c81a02eb8ef2fb537115c1b25cfaa6d2d8",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2011-01-21T08:57:45Z",
    "title_canon_sha256": "0cd87e21b2d0350424ec8582554df5cc8ac4115f7862b58e25c3a99b2eee8d0c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.4090",
    "kind": "arxiv",
    "version": 1
  }
}