Pith Number

pith:BK6D63RQ

pith:2019:BK6D63RQHBJ66FV5S6VJTCTAI5

not attested not anchored not stored refs pending

Double phase transonic flow problems with variable growth: nonlinear patterns and stationary waves

Anouar Bahrouni, Du\v{s}an D. Repov\v{s}, Vicen\c{t}iu D. R\u{a}dulescu

arxiv:1906.02609 v2 · 2019-06-06 · math.AP · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BK6D63RQHBJ66FV5S6VJTCTAI5}

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	2026-05-17T23:39:53.620425Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0abc3f6e303853ef16bd97aa998a604751f4571af7ba7bbe52292a7dce2e4d07

Aliases

arxiv: 1906.02609 · arxiv_version: 1906.02609v2 · doi: 10.48550/arxiv.1906.02609 · pith_short_12: BK6D63RQHBJ6 · pith_short_16: BK6D63RQHBJ66FV5 · pith_short_8: BK6D63RQ

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/BK6D63RQHBJ66FV5S6VJTCTAI5 \
  | 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: 0abc3f6e303853ef16bd97aa998a604751f4571af7ba7bbe52292a7dce2e4d07

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e71540e9376d4436b4655e69b1645f6a502a67d8f2581ef048a514be519d4a9a",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2019-06-06T15:48:30Z",
    "title_canon_sha256": "94d06b46711d73dbf18e84dd788d640f2626786dcbf569f6906c880922af60c7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1906.02609",
    "kind": "arxiv",
    "version": 2
  }
}