Pith Number

pith:26ZMWZUL

pith:2015:26ZMWZUL75KHTQHZV6UG7Q425C

not attested not anchored not stored refs pending

Sobolev spaces adapted to the Schr\"odinger operator with inverse-square potential

C. Miao, J. Zhang, J. Zheng, M. Visan, R. Killip

arxiv:1503.02716 v2 · 2015-03-09 · 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{26ZMWZUL75KHTQHZV6UG7Q425C}

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	2026-05-18T01:17:20.587295Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d7b2cb668bff5479c0f9afa86fc39ae8aaef5c06e549af077c2001719d536133

Aliases

arxiv: 1503.02716 · arxiv_version: 1503.02716v2 · doi: 10.48550/arxiv.1503.02716 · pith_short_12: 26ZMWZUL75KH · pith_short_16: 26ZMWZUL75KHTQHZ · pith_short_8: 26ZMWZUL

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/26ZMWZUL75KHTQHZV6UG7Q425C \
  | 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: d7b2cb668bff5479c0f9afa86fc39ae8aaef5c06e549af077c2001719d536133

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2b67f731b47c7c1d057ec2ef3452fe9632172193a8d13b4f4f28b4df206c2978",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-03-09T22:35:05Z",
    "title_canon_sha256": "d0bf98352eb05acc6b6545496dcfe68f3fc93f2788eb648ad1197fd48e4da6c3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.02716",
    "kind": "arxiv",
    "version": 2
  }
}