Pith Number

pith:FELH6AGE

pith:2016:FELH6AGE6E5ASD6NNFJSWVPLNJ

not attested not anchored not stored refs pending

Inclusion relations between Modulation and Triebel-Lizorkin spaces

Guoping Zhao, Huoxiong Wu, Weichao Guo

arxiv:1609.05278 v1 · 2016-09-17 · 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{FELH6AGE6E5ASD6NNFJSWVPLNJ}

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	2026-05-18T01:04:26.877797Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

29167f00c4f13a090fcd69532b55eb6a40519c0160424d6f1475282008c293c3

Aliases

arxiv: 1609.05278 · arxiv_version: 1609.05278v1 · doi: 10.48550/arxiv.1609.05278 · pith_short_12: FELH6AGE6E5A · pith_short_16: FELH6AGE6E5ASD6N · pith_short_8: FELH6AGE

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/FELH6AGE6E5ASD6NNFJSWVPLNJ \
  | 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: 29167f00c4f13a090fcd69532b55eb6a40519c0160424d6f1475282008c293c3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "111ad561fe59de5bc9ff75d4b45faab8973dfa3249f4a29ee80e46b931d05939",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2016-09-17T03:47:59Z",
    "title_canon_sha256": "6108c77cb4f84f3748fd75b43fc9926aa215edfdf4f629e9d522857844f2864c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.05278",
    "kind": "arxiv",
    "version": 1
  }
}