Pith Number

pith:2A77GFRR

pith:2016:2A77GFRRY5AO4UHGBS5Q7GQ46R

not attested not anchored not stored refs pending

Best approximations and moduli of smoothness of functions and their derivatives in $L_p$, $0<p<1$

Yurii Kolomoitsev

arxiv:1612.08020 v1 · 2016-12-23 · 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{2A77GFRRY5AO4UHGBS5Q7GQ46R}

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	2026-05-18T00:54:05.078690Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d03ff31631c740ee50e60cbb0f9a1cf455d5a3c8412f2c66272af41973885830

Aliases

arxiv: 1612.08020 · arxiv_version: 1612.08020v1 · doi: 10.48550/arxiv.1612.08020 · pith_short_12: 2A77GFRRY5AO · pith_short_16: 2A77GFRRY5AO4UHG · pith_short_8: 2A77GFRR

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/2A77GFRRY5AO4UHGBS5Q7GQ46R \
  | 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: d03ff31631c740ee50e60cbb0f9a1cf455d5a3c8412f2c66272af41973885830

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7706b9343672447c5a4ec6867b5d1ed6d43bcca7b53d77333aa026cd8a6f23f3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2016-12-23T16:03:40Z",
    "title_canon_sha256": "a26032b313b340820daf9aa795f87a702a2556629c904e23150e39daddd1a88f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.08020",
    "kind": "arxiv",
    "version": 1
  }
}