Pith Number

pith:ZA2SOGQN

pith:2008:ZA2SOGQN6UG425U7V3G6ZKVTFC

not attested not anchored not stored refs pending

Retarded integral inequalities of Gronwall-Bihari type

Delfim F. M. Torres, Rui A. C. Ferreira

arxiv:0806.4709 v1 · 2008-06-28 · 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{ZA2SOGQN6UG425U7V3G6ZKVTFC}

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	2026-05-18T03:41:40.624826Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c835271a0df50dcd769faecdecaab328a4962c40887a1b2df4f0dd25b42fb34f

Aliases

arxiv: 0806.4709 · arxiv_version: 0806.4709v1 · doi: 10.48550/arxiv.0806.4709 · pith_short_12: ZA2SOGQN6UG4 · pith_short_16: ZA2SOGQN6UG425U7 · pith_short_8: ZA2SOGQN

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/ZA2SOGQN6UG425U7V3G6ZKVTFC \
  | 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: c835271a0df50dcd769faecdecaab328a4962c40887a1b2df4f0dd25b42fb34f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e7d916427a4a13cbaa6b3e7c2dc1373d0380cf5914fd95d484379a3f492e4e1c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2008-06-28T17:26:06Z",
    "title_canon_sha256": "0e98c1fceb5ff638288408d375a4b15928097328f86b85b280127a35bbe33355"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0806.4709",
    "kind": "arxiv",
    "version": 1
  }
}