Pith Number

pith:YQBB4CC6

pith:2006:YQBB4CC6R2NBGFAWSFHCMUP4LM

not attested not anchored not stored refs pending

Sharp two-sided heat kernel estimates for critical Schr\"odinger operators on bounded domains

Achilles Tertikas, Luisa Moschini, Stathis Filippas

arxiv:math/0606151 v1 · 2006-06-07 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YQBB4CC6R2NBGFAWSFHCMUP4LM}

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	2026-05-18T01:38:24.041329Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c4021e085e8e9a131416914e2651fc5b359135e9fb791db4507643ac10b0bac8

Aliases

arxiv: math/0606151 · arxiv_version: math/0606151v1 · doi: 10.48550/arxiv.math/0606151 · pith_short_12: YQBB4CC6R2NB · pith_short_16: YQBB4CC6R2NBGFAW · pith_short_8: YQBB4CC6

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/YQBB4CC6R2NBGFAWSFHCMUP4LM \
  | 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: c4021e085e8e9a131416914e2651fc5b359135e9fb791db4507643ac10b0bac8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ab4cdff6aba369ebcbb3ff5e17ebdec7553922e1b47ddce1da1bbf56ff27f490",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.AP",
    "submitted_at": "2006-06-07T12:47:19Z",
    "title_canon_sha256": "4c18c2fd1d1b4bd7afd6ce973cfccb1139776e21058d8a7141c504e0af65acb4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0606151",
    "kind": "arxiv",
    "version": 1
  }
}