Pith Number

pith:BRXZL4FE

pith:2015:BRXZL4FEHGB5VX4NXXELTLDPAU

not attested not anchored not stored refs pending

Atomic and molecular decompositions in variable exponent 2-microlocal spaces and applications

Alexandre Almeida, Ant\'onio Caetano

arxiv:1508.02364 v3 · 2015-08-10 · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BRXZL4FEHGB5VX4NXXELTLDPAU}

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	2026-05-18T01:24:06.600927Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0c6f95f0a43983dadf8dbdc8b9ac6f053371ff130a3c1f7e71427d3db9d21ba2

Aliases

arxiv: 1508.02364 · arxiv_version: 1508.02364v3 · doi: 10.48550/arxiv.1508.02364 · pith_short_12: BRXZL4FEHGB5 · pith_short_16: BRXZL4FEHGB5VX4N · pith_short_8: BRXZL4FE

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/BRXZL4FEHGB5VX4NXXELTLDPAU \
  | 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: 0c6f95f0a43983dadf8dbdc8b9ac6f053371ff130a3c1f7e71427d3db9d21ba2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "62b326f5c5156264ba6af9b203a61084404fa89e7aaaa67bd80033cc5c16fe08",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2015-08-10T19:21:39Z",
    "title_canon_sha256": "b7ef6a5d50963a1b2d68b64bf5a4efd7313544d08af6e6e5d3083aa03b42c6f0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.02364",
    "kind": "arxiv",
    "version": 3
  }
}