Pith Number

pith:S4W5ZNJT

pith:2011:S4W5ZNJT3EFYGWL5MFZKQINSYK

not attested not anchored not stored refs pending

Tail behavior of solutions of linear recursions on trees

Mariana Olvera-Cravioto

arxiv:1108.3809 v1 · 2011-08-18 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{S4W5ZNJT3EFYGWL5MFZKQINSYK}

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	2026-05-18T04:15:07.436087Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

972ddcb533d90b83597d6172a821b2c2a8a92020112d264ec0146b3e6ad92fc1

Aliases

arxiv: 1108.3809 · arxiv_version: 1108.3809v1 · doi: 10.48550/arxiv.1108.3809 · pith_short_12: S4W5ZNJT3EFY · pith_short_16: S4W5ZNJT3EFYGWL5 · pith_short_8: S4W5ZNJT

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/S4W5ZNJT3EFYGWL5MFZKQINSYK \
  | 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: 972ddcb533d90b83597d6172a821b2c2a8a92020112d264ec0146b3e6ad92fc1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aa4e2bf7a3f79f2bf604c48b741c31299cc9b66c7361bf605a256e9bd4381bec",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-08-18T18:49:46Z",
    "title_canon_sha256": "302d3c316b7acd373ab53a29bf947a4d3d75a6ba23638e8340f82a0d18884c32"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.3809",
    "kind": "arxiv",
    "version": 1
  }
}