Pith Number

pith:HHUZPQGB

pith:2024:HHUZPQGBX37ZV5R75II7NYNEPG

not attested not anchored not stored refs pending

The monopolist's free boundary problem in the plane

Cale Rankin, Kelvin Shuangjian Zhang, Robert J. McCann

arxiv:2412.15505 v3 · 2024-12-20 · math.AP · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HHUZPQGBX37ZV5R75II7NYNEPG}

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	2026-06-24T01:14:19.446051Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

39e997c0c1beff9af63fea11f6e1a4799180a2668f86c506feebe5f6ccef2827

Aliases

arxiv: 2412.15505 · arxiv_version: 2412.15505v3 · doi: 10.48550/arxiv.2412.15505 · pith_short_12: HHUZPQGBX37Z · pith_short_16: HHUZPQGBX37ZV5R7 · pith_short_8: HHUZPQGB

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/HHUZPQGBX37ZV5R75II7NYNEPG \
  | 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: 39e997c0c1beff9af63fea11f6e1a4799180a2668f86c506feebe5f6ccef2827

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4dc8e213384db72fe7fe84db77143011119daa8e9639cb7aff0bee4a803f4254",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2024-12-20T02:36:56Z",
    "title_canon_sha256": "2b7d81c4a532d9da8ef0bf4ea5399022e4dc566b8aa764c6963b23f45f75d194"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.15505",
    "kind": "arxiv",
    "version": 3
  }
}