Pith Number

pith:XCPZROX6

pith:2025:XCPZROX64CTCOKBNHOVOPSKXD2

not attested not anchored not stored refs pending

Uniqueness of Transonic Shock Solutions for Two-Dimensional Steady Compressible Euler Flows in an Expanding Nozzle

Beixiang Fang, Wei Xiang, Xin Gao

arxiv:2502.06199 v1 · 2025-02-10 · 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{XCPZROX64CTCOKBNHOVOPSKXD2}

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	2026-07-05T10:11:48.971619Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b89f98bafee0a627282d3baae7c9571ebde48cdfab00f25498cd5c1b4c79cf39

Aliases

arxiv: 2502.06199 · arxiv_version: 2502.06199v1 · doi: 10.48550/arxiv.2502.06199 · pith_short_12: XCPZROX64CTC · pith_short_16: XCPZROX64CTCOKBN · pith_short_8: XCPZROX6

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/XCPZROX64CTCOKBNHOVOPSKXD2 \
  | 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: b89f98bafee0a627282d3baae7c9571ebde48cdfab00f25498cd5c1b4c79cf39

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e1276eb6b01f41440f9c0d6e604e977322272ac3b2a329fff1bce6cfbc6e2972",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-02-10T06:52:33Z",
    "title_canon_sha256": "920e563f1b09693abcbc77985b0d350c214503a8c9d2d2dae02f7a2f692f6fdd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2502.06199",
    "kind": "arxiv",
    "version": 1
  }
}