Pith Number

pith:M2U5DMH4

pith:2013:M2U5DMH4FXSOWYYLPOAAITLDAH

not attested not anchored not stored refs pending

Efficient pseudo-spectral solvers for the PKN model of hydrofracturing

Gennady Mishuris, Michal Wrobel

arxiv:1302.1209 v2 · 2013-02-05 · math.NA · physics.flu-dyn · physics.geo-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{M2U5DMH4FXSOWYYLPOAAITLDAH}

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	2026-05-18T03:30:01.995776Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

66a9d1b0fc2de4eb630b7b80044d6301f22b5351fe13c55598644ad91b6e17e8

Aliases

arxiv: 1302.1209 · arxiv_version: 1302.1209v2 · doi: 10.48550/arxiv.1302.1209 · pith_short_12: M2U5DMH4FXSO · pith_short_16: M2U5DMH4FXSOWYYL · pith_short_8: M2U5DMH4

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/M2U5DMH4FXSOWYYLPOAAITLDAH \
  | 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: 66a9d1b0fc2de4eb630b7b80044d6301f22b5351fe13c55598644ad91b6e17e8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e6ae3f59038e05e890a7518b002a2c007013abfa9f5f1cfe68ac7d450d372bc8",
    "cross_cats_sorted": [
      "physics.flu-dyn",
      "physics.geo-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2013-02-05T21:13:42Z",
    "title_canon_sha256": "adf72fafd714159a6f3d26eef42d8a7edf91502faf87677e203dbffabdde9426"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.1209",
    "kind": "arxiv",
    "version": 2
  }
}