Pith Number

pith:3PT4PCPE

pith:2017:3PT4PCPE64PYVJPUYRIBCP42YR

not attested not anchored not stored refs pending

Extension and approximation of $m$-subharmonic functions

Lisa Hed, Per Ahag, Rafal Czyz

arxiv:1703.03181 v1 · 2017-03-09 · math.CV · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3PT4PCPE64PYVJPUYRIBCP42YR}

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	2026-05-18T00:06:56.593340Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dbe7c789e4f71f8aa5f4c450113f9ac4665e0cb8c0373d9c78911ff9ea8b1b13

Aliases

arxiv: 1703.03181 · arxiv_version: 1703.03181v1 · doi: 10.48550/arxiv.1703.03181 · pith_short_12: 3PT4PCPE64PY · pith_short_16: 3PT4PCPE64PYVJPU · pith_short_8: 3PT4PCPE

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/3PT4PCPE64PYVJPUYRIBCP42YR \
  | 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: dbe7c789e4f71f8aa5f4c450113f9ac4665e0cb8c0373d9c78911ff9ea8b1b13

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "45d0d3a43ca6332ed4d500125fe0a2918387222d548c1c9ba43e54ac5e47a555",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2017-03-09T08:55:42Z",
    "title_canon_sha256": "82cd877573971ddfbbca9a6062ac3c54e2a28762c99be1c0c94c57aad8a8fff9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1703.03181",
    "kind": "arxiv",
    "version": 1
  }
}