Pith Number

pith:IP443O2A

pith:2015:IP443O2ALEBRV2ULIM5XGJZB6R

not attested not anchored not stored refs pending

The Abresch-Rosenberg Shape Operator and applications

Haimer A. Trejos, Jos\'e M. Espinar

arxiv:1512.02099 v3 · 2015-12-07 · 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{IP443O2ALEBRV2ULIM5XGJZB6R}

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	2026-05-18T01:12:12.755241Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

43f9cdbb4059031aea8b433b732721f45b13ae213341e7b9386ab2aca9a56e7a

Aliases

arxiv: 1512.02099 · arxiv_version: 1512.02099v3 · doi: 10.48550/arxiv.1512.02099 · pith_short_12: IP443O2ALEBR · pith_short_16: IP443O2ALEBRV2UL · pith_short_8: IP443O2A

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/IP443O2ALEBRV2ULIM5XGJZB6R \
  | 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: 43f9cdbb4059031aea8b433b732721f45b13ae213341e7b9386ab2aca9a56e7a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "06c20ce8ea468ab53383aaaef23574ec4839b78e3750db3d22494be70d279c84",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2015-12-07T15:51:41Z",
    "title_canon_sha256": "c1cd05fa1e1fc1362e9f930af91d4f32ee6fc3bfa208a287664d412ccc11e20f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.02099",
    "kind": "arxiv",
    "version": 3
  }
}