Pith Number

pith:QRJUN4YU

pith:2024:QRJUN4YUTIRELZUO7WRCWJILBR

not attested not anchored not stored refs pending

Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler

Isaac Neal, Steve Shkoller, Vlad Vicol

arxiv:2412.21040 v2 · 2024-12-30 · 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{QRJUN4YUTIRELZUO7WRCWJILBR}

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	2026-07-05T09:56:05.071835Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

845346f3149a2245e68efda22b250b0c7b8cc62dd52dc131ef3d45b53bde66ea

Aliases

arxiv: 2412.21040 · arxiv_version: 2412.21040v2 · doi: 10.48550/arxiv.2412.21040 · pith_short_12: QRJUN4YUTIRE · pith_short_16: QRJUN4YUTIRELZUO · pith_short_8: QRJUN4YU

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/QRJUN4YUTIRELZUO7WRCWJILBR \
  | 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: 845346f3149a2245e68efda22b250b0c7b8cc62dd52dc131ef3d45b53bde66ea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6237578b3dab24810aa73344685eb83417f6e654747096392de68eaf4c4e1344",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2024-12-30T16:03:56Z",
    "title_canon_sha256": "57684308a5773ac0a1f775116ac8540f379a8ff473f4c72e6e507b6358cfca9b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.21040",
    "kind": "arxiv",
    "version": 2
  }
}