Pith Number

pith:6PBTSVAR

pith:2018:6PBTSVARJ4KNLXEFUW5SB4MSGC

not attested not anchored not stored refs pending

Primary singularities of vector fields on surfaces

Francisco-Javier Turiel, Morris W. Hirsch

arxiv:1807.04533 v1 · 2018-07-12 · 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{6PBTSVARJ4KNLXEFUW5SB4MSGC}

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	2026-05-18T00:10:53.169384Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f3c33954114f14d5dc85a5bb20f19230882b9e94d7deba40c2a9514b5880df68

Aliases

arxiv: 1807.04533 · arxiv_version: 1807.04533v1 · doi: 10.48550/arxiv.1807.04533 · pith_short_12: 6PBTSVARJ4KN · pith_short_16: 6PBTSVARJ4KNLXEF · pith_short_8: 6PBTSVAR

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/6PBTSVARJ4KNLXEFUW5SB4MSGC \
  | 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: f3c33954114f14d5dc85a5bb20f19230882b9e94d7deba40c2a9514b5880df68

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a26a350c63b6ba6246e45b0e8a1c52cfa3b3b48738da0e8d7d6fe4068d58d686",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2018-07-12T10:50:47Z",
    "title_canon_sha256": "d4a68bda01f0c33a9f76570bf1ad9ccb28c1cb9729919f398a4c45ac95167bd3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1807.04533",
    "kind": "arxiv",
    "version": 1
  }
}