Pith Number

pith:FMDM5X6V

pith:2016:FMDM5X6VIBYNXTT2WL766HO7BQ

not attested not anchored not stored refs pending

Sharp $L^p$ estimates for Schr\"odinger groups on spaces of homogeneous type

Fabio Nicola, Piero D'Ancona, The Anh Bui

arxiv:1612.01267 v3 · 2016-12-05 · math.AP · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FMDM5X6VIBYNXTT2WL766HO7BQ}

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	2026-05-17T23:39:42.304112Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2b06cedfd54070dbce7ab2ffef1ddf0c0da76b4a225be8d3fb348a722e5c1c4e

Aliases

arxiv: 1612.01267 · arxiv_version: 1612.01267v3 · doi: 10.48550/arxiv.1612.01267 · pith_short_12: FMDM5X6VIBYN · pith_short_16: FMDM5X6VIBYNXTT2 · pith_short_8: FMDM5X6V

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/FMDM5X6VIBYNXTT2WL766HO7BQ \
  | 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: 2b06cedfd54070dbce7ab2ffef1ddf0c0da76b4a225be8d3fb348a722e5c1c4e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1232a5c33388964f870641db2e08974448da7f1dbd025cd8dfcfc5e9f2bcbf97",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-12-05T08:01:18Z",
    "title_canon_sha256": "fa588bb4b9f08c12c0753d73566623f37a5827b5ecf7812728b2831cf3e09915"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.01267",
    "kind": "arxiv",
    "version": 3
  }
}