Pith Number

pith:R73UPUBH

pith:2023:R73UPUBHJRY6HSZ2J4JODLBWGX

not attested not anchored not stored refs pending

L2 to Lp bounds for spectral projectors on thin intervals in Riemannian manifolds

Pierre Germain

arxiv:2306.16981 v1 · 2023-06-29 · math.AP · 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{R73UPUBHJRY6HSZ2J4JODLBWGX}

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.

Cited by

1 paper in Pith

$L^4$ norm of spectral projectors on polynomially small frequency intervals for $S^1$-symmetric surfaces

Receipt and verification

First computed	2026-07-05T06:26:11.838327Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8ff747d0274c71e3cb3a4f12e1ac3635e9e69f25f1cbd9cafad0deba8563accf

Aliases

arxiv: 2306.16981 · arxiv_version: 2306.16981v1 · doi: 10.48550/arxiv.2306.16981 · pith_short_12: R73UPUBHJRY6 · pith_short_16: R73UPUBHJRY6HSZ2 · pith_short_8: R73UPUBH

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/R73UPUBHJRY6HSZ2J4JODLBWGX \
  | 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: 8ff747d0274c71e3cb3a4f12e1ac3635e9e69f25f1cbd9cafad0deba8563accf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4e81c67658c9d128e293b052e1ec6c30461ec48a63fd3c23899597993877ed4b",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2023-06-29T14:37:48Z",
    "title_canon_sha256": "1b6f3af1f0cd94e19b5629d10661fb350072c6fdf5f91079a05eed17d3081403"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2306.16981",
    "kind": "arxiv",
    "version": 1
  }
}