Pith Number

pith:ERGNEXQB

pith:2016:ERGNEXQBO2FUAMD3ALPYDHHSQB

not attested not anchored not stored refs pending

Lower bounds on the moduli of three-dimensional Coulomb-Dirac operators via fractional Laplacians with applications

David M\"uller, Sergey Morozov

arxiv:1612.06591 v1 · 2016-12-20 · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ERGNEXQBO2FUAMD3ALPYDHHSQB}

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	2026-05-18T00:35:24.133270Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

244cd25e01768b40307b02df819cf2804fdf832673522894dfae9a53622444d7

Aliases

arxiv: 1612.06591 · arxiv_version: 1612.06591v1 · doi: 10.48550/arxiv.1612.06591 · pith_short_12: ERGNEXQBO2FU · pith_short_16: ERGNEXQBO2FUAMD3 · pith_short_8: ERGNEXQB

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/ERGNEXQBO2FUAMD3ALPYDHHSQB \
  | 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: 244cd25e01768b40307b02df819cf2804fdf832673522894dfae9a53622444d7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "894c0d5506c8100187071b30e369e4c94335528f4a82378260c8063d53d896c1",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2016-12-20T10:26:54Z",
    "title_canon_sha256": "197974ffc2f180352d4b564f5f7f6302d153dcd68fd196afb24884a35426e179"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.06591",
    "kind": "arxiv",
    "version": 1
  }
}