Pith Number

pith:KPHTCNLU

pith:2007:KPHTCNLU6IY74MS244EA4SQ7GH

not attested not anchored not stored refs pending

The Riemann problem for the shallow water equations with discontinuous topography

Mai-Duc Thanh, Philippe G. LeFloch

arxiv:0712.3778 v1 · 2007-12-21 · math.AP · cs.NA · math.NA · physics.flu-dyn

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KPHTCNLU6IY74MS244EA4SQ7GH}

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	2026-06-03T22:06:03.788926Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

53cf313574f231fe325ae7080e4a1f31e6f3fd511dcad9669b69c18d8f3271bd

Aliases

arxiv: 0712.3778 · arxiv_version: 0712.3778v1 · doi: 10.48550/arxiv.0712.3778 · pith_short_12: KPHTCNLU6IY7 · pith_short_16: KPHTCNLU6IY74MS2 · pith_short_8: KPHTCNLU

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/KPHTCNLU6IY74MS244EA4SQ7GH \
  | 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: 53cf313574f231fe325ae7080e4a1f31e6f3fd511dcad9669b69c18d8f3271bd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c0ccd0a6492623cf2f1f2ee2a9b41ba5fdeb8739e351c1550674e847384f469e",
    "cross_cats_sorted": [
      "cs.NA",
      "math.NA",
      "physics.flu-dyn"
    ],
    "license": "",
    "primary_cat": "math.AP",
    "submitted_at": "2007-12-21T19:25:50Z",
    "title_canon_sha256": "583d385d4d27317558015bb789dfa4df15bd9481a7fa28d31fe975f3b9651c7a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0712.3778",
    "kind": "arxiv",
    "version": 1
  }
}