Pith Number

pith:J7ZLWM2M

pith:2026:J7ZLWM2M5KWOMUWE3TLNOVZU72

not attested not anchored not stored refs pending

Unidirectional Entropic Solutions of the Pressureless Euler Alignment System

Joshua O. Adeleke, Trevor M. Leslie

arxiv:2606.11159 v1 · 2026-06-09 · 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{J7ZLWM2M5KWOMUWE3TLNOVZU72}

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	2026-06-10T01:11:14.521442Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4ff2bb334ceaace652c4dcd6d75734fe95cc93cd5aec597e2666d16b4c87846f

Aliases

arxiv: 2606.11159 · arxiv_version: 2606.11159v1 · doi: 10.48550/arxiv.2606.11159 · pith_short_12: J7ZLWM2M5KWO · pith_short_16: J7ZLWM2M5KWOMUWE · pith_short_8: J7ZLWM2M

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/J7ZLWM2M5KWOMUWE3TLNOVZU72 \
  | 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: 4ff2bb334ceaace652c4dcd6d75734fe95cc93cd5aec597e2666d16b4c87846f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a1ee786403f1413f7f2614f4a38ce07685dc7529403ec53f9cd9f996c524b8b7",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-06-09T17:41:34Z",
    "title_canon_sha256": "ee4a7243c8ad95282ed819a6a3859ccb0ab0d3af8ddbc3570e62f27c311bfa36"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.11159",
    "kind": "arxiv",
    "version": 1
  }
}