Pith Number

pith:B72LR5GJ

pith:2010:B72LR5GJ332WPRUK7TBED4ZXC5

not attested not anchored not stored refs pending

Polynomial approximation, local polynomial convexity, and degenerate CR singularities -- II

Gautam Bharali

arxiv:1010.5205 v2 · 2010-10-25 · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{B72LR5GJ332WPRUK7TBED4ZXC5}

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	2026-05-18T01:34:42.479311Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0ff4b8f4c9def567c68afcc241f3371778f4d9213d2b7d44ba2fa58704bfd4c0

Aliases

arxiv: 1010.5205 · arxiv_version: 1010.5205v2 · doi: 10.48550/arxiv.1010.5205 · pith_short_12: B72LR5GJ332W · pith_short_16: B72LR5GJ332WPRUK · pith_short_8: B72LR5GJ

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/B72LR5GJ332WPRUK7TBED4ZXC5 \
  | 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: 0ff4b8f4c9def567c68afcc241f3371778f4d9213d2b7d44ba2fa58704bfd4c0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "013bc0d1405d8c59e17074222bd67bb2d9f159dbb2b3a959f9377df8d8039d4c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2010-10-25T17:47:29Z",
    "title_canon_sha256": "741f9649a64f3232f9611f0eca9086ef011970c259348bb5f05aa4ca8cdb6101"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.5205",
    "kind": "arxiv",
    "version": 2
  }
}