Pith Number

pith:FO33PMNA

pith:2026:FO33PMNA75GCBUPUDOEGUCJAUF

not attested not anchored not stored refs pending

The Geometry of Phase Transitions in Generative Dynamics via Projection Caustics

Kotaro Sakamoto, Ryosuke Sakamoto

arxiv:2606.13191 v1 · 2026-06-11 · cs.LG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FO33PMNA75GCBUPUDOEGUCJAUF}

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	2026-06-12T01:09:46.034486Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2bb7b7b1a0ff4c20d1f41b886a0920a1670261456b3dd0c147543877b1192a22

Aliases

arxiv: 2606.13191 · arxiv_version: 2606.13191v1 · doi: 10.48550/arxiv.2606.13191 · pith_short_12: FO33PMNA75GC · pith_short_16: FO33PMNA75GCBUPU · pith_short_8: FO33PMNA

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/FO33PMNA75GCBUPUDOEGUCJAUF \
  | 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: 2bb7b7b1a0ff4c20d1f41b886a0920a1670261456b3dd0c147543877b1192a22

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a680537e13086dc1a1b73c1065a2d8f6219fe76ae5fd7c4ff12fb71b68612185",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-06-11T10:59:18Z",
    "title_canon_sha256": "0a9bb4aa59265d49b9c89cdab0b0b70d4e94103d4bfe96b1991b08f453057780"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.13191",
    "kind": "arxiv",
    "version": 1
  }
}