Pith Number

pith:MDHK4SQK

pith:2009:MDHK4SQKPSIVRHLIX3WD7NGYDN

not attested not anchored not stored refs pending

Global Strong Solutions of the Boltzmann Equation without Angular Cut-off

Philip T. Gressman, Robert M. Strain

arxiv:0912.0888 v2 · 2009-12-04 · math.AP · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MDHK4SQKPSIVRHLIX3WD7NGYDN}

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	2026-05-18T01:20:22.664343Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

60ceae4a0a7c91589d68beec3fb4d81b6fb6e8f3d713a5e0970b9cb68c58b00e

Aliases

arxiv: 0912.0888 · arxiv_version: 0912.0888v2 · doi: 10.48550/arxiv.0912.0888 · pith_short_12: MDHK4SQKPSIV · pith_short_16: MDHK4SQKPSIVRHLI · pith_short_8: MDHK4SQK

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/MDHK4SQKPSIVRHLIX3WD7NGYDN \
  | 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: 60ceae4a0a7c91589d68beec3fb4d81b6fb6e8f3d713a5e0970b9cb68c58b00e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "172b324bc41e7d2c7b5f4414eacd996fbd7eae9ccdb1fe740cd330b0bfa2f5e1",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2009-12-04T16:25:45Z",
    "title_canon_sha256": "9b4b73b6a558644a9acb37d6ea40b9ed1849d3b3c77eafafc2d712145691de53"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.0888",
    "kind": "arxiv",
    "version": 2
  }
}