Pith Number

pith:PAABD2DM

pith:2015:PAABD2DMKMEIC2PWLSYJHV4SKK

not attested not anchored not stored refs pending

Functions on the sphere with critical points in pairs and orthogonal geodesic chords

F. Giannoni, P. Piccione, R. Giamb\`o

arxiv:1503.06176 v1 · 2015-03-20 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PAABD2DMKMEIC2PWLSYJHV4SKK}

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	2026-05-18T02:20:48.407408Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

780011e86c53088169f65cb093d79252b605139ca16f7e5b03b6b988469b413d

Aliases

arxiv: 1503.06176 · arxiv_version: 1503.06176v1 · doi: 10.48550/arxiv.1503.06176 · pith_short_12: PAABD2DMKMEI · pith_short_16: PAABD2DMKMEIC2PW · pith_short_8: PAABD2DM

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/PAABD2DMKMEIC2PWLSYJHV4SKK \
  | 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: 780011e86c53088169f65cb093d79252b605139ca16f7e5b03b6b988469b413d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e479d5ccf8eae5e43dcb61a295d71e95b7444998f5906bb4098528c7ee65fb33",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-03-20T17:42:54Z",
    "title_canon_sha256": "ecb2195efbb2a96f0dcb4403746bd0ae0ef6cbb10dcc6ae4df511791a88913e2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.06176",
    "kind": "arxiv",
    "version": 1
  }
}