Pith Number

pith:WIWYV2DK

pith:2026:WIWYV2DKGZFQJIOXU6SFYKEGAN

not attested not anchored not stored refs pending

Invasion Fronts in Shifting Habitats and Competition Systems: A Hamilton-Jacobi Approach and Nonlocal Effects

Chang-Hong Wu, King-Yeung Lam, Xiao Yu

arxiv:2607.29001 v1 · 2026-07-31 · 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{WIWYV2DKGZFQJIOXU6SFYKEGAN}

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	2026-08-03T01:17:55.211437Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b22d8ae86a364b04a1d7a7a45c2886037a5912ca26110db4c143b977b4d7b7f2

Aliases

arxiv: 2607.29001 · arxiv_version: 2607.29001v1 · doi: 10.48550/arxiv.2607.29001 · pith_short_12: WIWYV2DKGZFQ · pith_short_16: WIWYV2DKGZFQJIOX · pith_short_8: WIWYV2DK

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/WIWYV2DKGZFQJIOXU6SFYKEGAN \
  | 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: b22d8ae86a364b04a1d7a7a45c2886037a5912ca26110db4c143b977b4d7b7f2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ea8318969739565d32b2a7b6e3854c91b770c779bad001c3aafb693e328ec4bb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-07-31T03:57:44Z",
    "title_canon_sha256": "af1a740b6cb0134516ec6b06cefc3e344dbc2fe011f310f801f6f9327810730d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.29001",
    "kind": "arxiv",
    "version": 1
  }
}