Pith Number

pith:PI44JQYX

pith:2020:PI44JQYXZIRQGPHIQEW3FC7M7Y

not attested not anchored not stored refs pending

Existence and non-existence for the collision-induced breakage equation

Ankik Kumar Giri, Philippe Lauren\c{c}ot (IMT)

arxiv:2012.14658 v2 · 2020-12-29 · 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{PI44JQYXZIRQGPHIQEW3FC7M7Y}

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	2026-07-05T03:19:41.432993Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a39c4c317ca23033ce8812db28becfe066428299434a5734357d8b73934ac63

Aliases

arxiv: 2012.14658 · arxiv_version: 2012.14658v2 · doi: 10.48550/arxiv.2012.14658 · pith_short_12: PI44JQYXZIRQ · pith_short_16: PI44JQYXZIRQGPHI · pith_short_8: PI44JQYX

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/PI44JQYXZIRQGPHIQEW3FC7M7Y \
  | 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: 7a39c4c317ca23033ce8812db28becfe066428299434a5734357d8b73934ac63

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a750887408d28ea48af3f9dc202e0aae7becb62a22c0bd1b41860d5ca0c747d2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2020-12-29T08:39:30Z",
    "title_canon_sha256": "a2ae2e56fec9dba5d88325f3367f72ffbdc566cce217b99c7b5932034f99b376"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2012.14658",
    "kind": "arxiv",
    "version": 2
  }
}