Pith Number

pith:TGHKP7WS

pith:2015:TGHKP7WS2CRNFL6BH5VY2BXKVL

not attested not anchored not stored refs pending

Sobolev and Max Norm Error Estimates for Gaussian Beam Superpositions

Hailiang Liu, Nicolay M. Tanushev, Olof Runborg

arxiv:1510.09120 v1 · 2015-10-30 · math.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TGHKP7WS2CRNFL6BH5VY2BXKVL}

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	2026-05-18T01:28:22.870264Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

998ea7fed2d0a2d2afc13f6b8d06eaaad221153331103ae6c61bba2ee1b15cae

Aliases

arxiv: 1510.09120 · arxiv_version: 1510.09120v1 · doi: 10.48550/arxiv.1510.09120 · pith_short_12: TGHKP7WS2CRN · pith_short_16: TGHKP7WS2CRNFL6B · pith_short_8: TGHKP7WS

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/TGHKP7WS2CRNFL6BH5VY2BXKVL \
  | 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: 998ea7fed2d0a2d2afc13f6b8d06eaaad221153331103ae6c61bba2ee1b15cae

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f08737dcaafbfd9ce3bdeb117562cf5059d19a42c41958e18b1d65e7bd2571fd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2015-10-30T15:24:23Z",
    "title_canon_sha256": "4def5b9cab4b96652b77c18bada4c60bd697abb8fc282c376986bf1657e4a512"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.09120",
    "kind": "arxiv",
    "version": 1
  }
}