Pith Number

pith:MV2GQ5K4

pith:2010:MV2GQ5K4JDHMAI4F5C5HGAVBFB

not attested not anchored not stored refs pending

Optimal bounds for self-similar solutions to coagulation equations with product kernel

Barbara Niethammer, Juan J.L. Velazquez

arxiv:1010.1857 v2 · 2010-10-09 · 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{MV2GQ5K4JDHMAI4F5C5HGAVBFB}

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	2026-05-18T04:28:56.661925Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

657468755c48cec02385e8ba7302a128428e698274e658faa5a97ac6fb25b53e

Aliases

arxiv: 1010.1857 · arxiv_version: 1010.1857v2 · doi: 10.48550/arxiv.1010.1857 · pith_short_12: MV2GQ5K4JDHM · pith_short_16: MV2GQ5K4JDHMAI4F · pith_short_8: MV2GQ5K4

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/MV2GQ5K4JDHMAI4F5C5HGAVBFB \
  | 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: 657468755c48cec02385e8ba7302a128428e698274e658faa5a97ac6fb25b53e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4d4673c92ce734968cac02a104b1b440fd9fd7a14c34c1dea9fdfcc779520283",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-10-09T16:29:31Z",
    "title_canon_sha256": "637fcf1aa6b91f8576f58bfa9b7e45ab319cff5d235f97cb3566bfeff56b1c2e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.1857",
    "kind": "arxiv",
    "version": 2
  }
}