Pith Number

pith:BB7YAALU

pith:2016:BB7YAALUU7NOTZLUDBJCXNVW6J

not attested not anchored not stored refs pending

On the number of singular points for planar multivalued harmonic functions

Francesco Ghiraldin, Luca Spolaor

arxiv:1601.01967 v1 · 2016-01-08 · 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{BB7YAALUU7NOTZLUDBJCXNVW6J}

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	2026-05-18T01:23:10.956790Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

087f800174a7dae9e57418522bb6b6f25ef23b8fcd3cbfa9977bb9dc3ff7dbc9

Aliases

arxiv: 1601.01967 · arxiv_version: 1601.01967v1 · doi: 10.48550/arxiv.1601.01967 · pith_short_12: BB7YAALUU7NO · pith_short_16: BB7YAALUU7NOTZLU · pith_short_8: BB7YAALU

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/BB7YAALUU7NOTZLUDBJCXNVW6J \
  | 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: 087f800174a7dae9e57418522bb6b6f25ef23b8fcd3cbfa9977bb9dc3ff7dbc9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ec274567b09e7113f9efcaf54336337e1a8d612936bb6d628708fe464f9e20b7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-01-08T18:30:40Z",
    "title_canon_sha256": "0885a404bf4d2b5d26d930bc0c4c08f00d943c0bb6f51ddb162ae808a6e2b626"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.01967",
    "kind": "arxiv",
    "version": 1
  }
}