Pith Number

pith:57FQPLMC

pith:2016:57FQPLMC64JQJ5Z7L4OMQ6SVBJ

not attested not anchored not stored refs pending

Area bounds for minimal surfaces in geodesic ball of hyperbolic space

Jingze Zhu

arxiv:1612.02722 v1 · 2016-12-08 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{57FQPLMC64JQJ5Z7L4OMQ6SVBJ}

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	2026-05-18T00:55:32.928201Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

efcb07ad82f71304f73f5f1cc87a550a70bf9be96e7e72dc0b048eba824cda9a

Aliases

arxiv: 1612.02722 · arxiv_version: 1612.02722v1 · doi: 10.48550/arxiv.1612.02722 · pith_short_12: 57FQPLMC64JQ · pith_short_16: 57FQPLMC64JQJ5Z7 · pith_short_8: 57FQPLMC

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/57FQPLMC64JQJ5Z7L4OMQ6SVBJ \
  | 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: efcb07ad82f71304f73f5f1cc87a550a70bf9be96e7e72dc0b048eba824cda9a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c87d592c8062eca3e6d8ca7c8847c7abc50610b3a973ecec6ea0ac501a55cdc9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2016-12-08T16:48:41Z",
    "title_canon_sha256": "291dc2083957237b446e228d174ed52f1696dd7c06ba80cb834715c675b0c9ea"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.02722",
    "kind": "arxiv",
    "version": 1
  }
}