Pith Number

pith:J7H2R7MR

pith:2025:J7H2R7MRYMFKDYAPQAALJ3WUR3

not attested not anchored not stored refs pending

Transonic Shocks for 2-D Steady Euler Flows with Large Gravity in a Nozzle for Polytropic Gases

Beixiang Fang, Qin Zhao, Wei Xiang, Xin Gao

arxiv:2502.12746 v2 · 2025-02-18 · 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{J7H2R7MRYMFKDYAPQAALJ3WUR3}

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	2026-07-05T10:44:43.147637Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4fcfa8fd91c30aa1e00f8000b4eed48eff4daf634c01ff8d478fb75515b860ce

Aliases

arxiv: 2502.12746 · arxiv_version: 2502.12746v2 · doi: 10.48550/arxiv.2502.12746 · pith_short_12: J7H2R7MRYMFK · pith_short_16: J7H2R7MRYMFKDYAP · pith_short_8: J7H2R7MR

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/J7H2R7MRYMFKDYAPQAALJ3WUR3 \
  | 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: 4fcfa8fd91c30aa1e00f8000b4eed48eff4daf634c01ff8d478fb75515b860ce

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ac32b9dfeda2387cca27c22270adf3b9da8eb19dbdd8d4dbb3be671a4c3408cf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-02-18T11:06:16Z",
    "title_canon_sha256": "42b72718a96fb3ca4441e399e9b8f2eae60af44a666a3319a916e5dce6e0c050"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2502.12746",
    "kind": "arxiv",
    "version": 2
  }
}