Pith Number

pith:FBZPGBQE

pith:2015:FBZPGBQEBLBZAEGBDM2CBRFU3I

not attested not anchored not stored refs pending

Markov-type inequalities and duality in weighted Sobolev spaces

Francisco Marcell\'an, Jos\'e M. Rodr\'iguez, Yamilet Quintana

arxiv:1501.06213 v1 · 2015-01-25 · 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{FBZPGBQEBLBZAEGBDM2CBRFU3I}

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	2026-05-18T02:28:42.054566Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2872f306040ac39010c11b3420c4b4da37e11607228e14bcd1d1f24698a9e912

Aliases

arxiv: 1501.06213 · arxiv_version: 1501.06213v1 · doi: 10.48550/arxiv.1501.06213 · pith_short_12: FBZPGBQEBLBZ · pith_short_16: FBZPGBQEBLBZAEGB · pith_short_8: FBZPGBQE

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/FBZPGBQEBLBZAEGBDM2CBRFU3I \
  | 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: 2872f306040ac39010c11b3420c4b4da37e11607228e14bcd1d1f24698a9e912

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b0def4595c8830dec9674ff07083ef5e295e303fe4f5e6c88530860f0d3de037",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-01-25T21:39:49Z",
    "title_canon_sha256": "7cc43d856c842c36de04603f8b0de5cab030b24c76b7f7361074a337d1ce19be"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.06213",
    "kind": "arxiv",
    "version": 1
  }
}