Pith Number

pith:JC6W4W3H

pith:2026:JC6W4W3HMRAJ7X4WSB7KZEDBNC

not attested not anchored not stored refs pending

The massless Boltzmann equation in Minkowski spacetime

Ernesto Nungesser, Ho Lee, John Stalker, Paul Tod

arxiv:2606.30437 v1 · 2026-06-29 · 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{JC6W4W3HMRAJ7X4WSB7KZEDBNC}

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	2026-06-30T02:18:15.140741Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

48bd6e5b6764409fdf96907eac906168800e1d6f80b3f34511eba0decff2925b

Aliases

arxiv: 2606.30437 · arxiv_version: 2606.30437v1 · doi: 10.48550/arxiv.2606.30437 · pith_short_12: JC6W4W3HMRAJ · pith_short_16: JC6W4W3HMRAJ7X4W · pith_short_8: JC6W4W3H

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/JC6W4W3HMRAJ7X4WSB7KZEDBNC \
  | 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: 48bd6e5b6764409fdf96907eac906168800e1d6f80b3f34511eba0decff2925b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fb224a727ec3cd12bd2a90f9edae7e931689336516ce19defcc295e07c5c5a45",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-06-29T15:13:26Z",
    "title_canon_sha256": "7d4d5f8407655dcd12569a76e9d1c08fd6d950685535d9bd46084a5d09fbf9e8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.30437",
    "kind": "arxiv",
    "version": 1
  }
}