Pith Number

pith:G4NSU4QM

pith:2026:G4NSU4QMAYT5A3NLAJ3Q2Q53RH

not attested not anchored not stored refs pending

Formation of quasi-singularities of shock and implosion type for compressible Euler flows

Hongyu Liu, Xieling Fan

arxiv:2606.29454 v1 · 2026-06-28 · 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{G4NSU4QMAYT5A3NLAJ3Q2Q53RH}

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	2026-06-30T01:18:07.152967Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

371b2a720c0627d06dab02770d43bb89e39e4e71f4b5c8ba166aa52a8df581f0

Aliases

arxiv: 2606.29454 · arxiv_version: 2606.29454v1 · doi: 10.48550/arxiv.2606.29454 · pith_short_12: G4NSU4QMAYT5 · pith_short_16: G4NSU4QMAYT5A3NL · pith_short_8: G4NSU4QM

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/G4NSU4QMAYT5A3NLAJ3Q2Q53RH \
  | 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: 371b2a720c0627d06dab02770d43bb89e39e4e71f4b5c8ba166aa52a8df581f0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bbaf4f66e7bb33f79ccd48348b10d9ac533a457c37287065236beba267c99230",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-06-28T15:18:02Z",
    "title_canon_sha256": "b9df231f4b5c893a15306766104132d1dfd16c9dc0ea3ce691322ab0997d4ccd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.29454",
    "kind": "arxiv",
    "version": 1
  }
}