Pith Number

pith:26ZISC4M

pith:2025:26ZISC4MWHSOSUNDSXZQFZV7RE

not attested not anchored not stored refs pending

Flocking as a second-order phase transition in self-aligning active crystals

Alexander P. Antonov, Hartmut L\"owen, Lorenzo Caprini, Marco Musacchio

arxiv:2506.12967 v1 · 2025-06-15 · cond-mat.soft · cond-mat.stat-mech

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{26ZISC4MWHSOSUNDSXZQFZV7RE}

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.

Cited by

1 paper in Pith

Lattice-dependent orientational order in active crystals

Receipt and verification

First computed	2026-07-05T11:22:03.116674Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d7b2890b8cb1e4e951a395f302e6bf892ba22484e8ba560b37f973423dfd96d3

Aliases

arxiv: 2506.12967 · arxiv_version: 2506.12967v1 · doi: 10.48550/arxiv.2506.12967 · pith_short_12: 26ZISC4MWHSO · pith_short_16: 26ZISC4MWHSOSUND · pith_short_8: 26ZISC4M

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/26ZISC4MWHSOSUNDSXZQFZV7RE \
  | 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: d7b2890b8cb1e4e951a395f302e6bf892ba22484e8ba560b37f973423dfd96d3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ab675a08c57732911b69b36c279789c4326b6dd0a8f314d3d240268aad201dd3",
    "cross_cats_sorted": [
      "cond-mat.stat-mech"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.soft",
    "submitted_at": "2025-06-15T21:20:43Z",
    "title_canon_sha256": "437175b49389c69279b1b318bd6f792ab49d536ddb5b991c8ff2164fa1e7724b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.12967",
    "kind": "arxiv",
    "version": 1
  }
}