Pith Number

pith:CRNBR2CI

pith:2011:CRNBR2CITD2SB4N3ODPAHSJ7C7

not attested not anchored not stored refs pending

Range Expansion with Mutation and Selection: Dynamical Phase Transition in a Two-Species Eden Model

Erwin Frey, Jan-Timm Kuhr, Madeleine Leisner

arxiv:1110.2639 v3 · 2011-10-12 · cond-mat.stat-mech · q-bio.PE

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CRNBR2CITD2SB4N3ODPAHSJ7C7}

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	2026-05-18T04:08:23.702164Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

145a18e84898f520f1bb70de03c93f17e2270e67c4b59ae0241c71e417dad3f3

Aliases

arxiv: 1110.2639 · arxiv_version: 1110.2639v3 · doi: 10.48550/arxiv.1110.2639 · pith_short_12: CRNBR2CITD2S · pith_short_16: CRNBR2CITD2SB4N3 · pith_short_8: CRNBR2CI

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/CRNBR2CITD2SB4N3ODPAHSJ7C7 \
  | 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: 145a18e84898f520f1bb70de03c93f17e2270e67c4b59ae0241c71e417dad3f3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7b899998dcf4930f310e192c7579b34c6efa2be58027a809e241745f86b15f1e",
    "cross_cats_sorted": [
      "q-bio.PE"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2011-10-12T12:15:31Z",
    "title_canon_sha256": "a89fdaf5d6d215f1dc5c9aa2788783f7aedba032a127f17e3c2ca16ffd9b0377"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.2639",
    "kind": "arxiv",
    "version": 3
  }
}