Pith Number

pith:LYJJ3VL5

pith:2017:LYJJ3VL5K7ALW7TI4B6TSHPAOZ

not attested not anchored not stored refs pending

Logarithmic improvements in $L^{p}$ bounds for eigenfunctions at the critical exponent in the presence of nonpositive curvature

Christopher D. Sogge, Matthew D. Blair

arxiv:1706.06704 v2 · 2017-06-20 · math.AP · math.CA · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LYJJ3VL5K7ALW7TI4B6TSHPAOZ}

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	2026-05-18T00:11:00.524645Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5e129dd57d57c0bb7e68e07d391de07672b75cd6e3d24840bdd1f318c69f8989

Aliases

arxiv: 1706.06704 · arxiv_version: 1706.06704v2 · doi: 10.48550/arxiv.1706.06704 · pith_short_12: LYJJ3VL5K7AL · pith_short_16: LYJJ3VL5K7ALW7TI · pith_short_8: LYJJ3VL5

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/LYJJ3VL5K7ALW7TI4B6TSHPAOZ \
  | 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: 5e129dd57d57c0bb7e68e07d391de07672b75cd6e3d24840bdd1f318c69f8989

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ccbf87db419ab295c1007d381f77f95519968db207d5e625ffb2cd170c58d312",
    "cross_cats_sorted": [
      "math.CA",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2017-06-20T23:50:00Z",
    "title_canon_sha256": "81eca2265852a53925073a2328b0a41ae0b0677f2da99af25a056e3c87ab0e22"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1706.06704",
    "kind": "arxiv",
    "version": 2
  }
}