Pith Number

pith:VIVIOXFT

pith:2015:VIVIOXFTZGKI7BW4CSQPQANN22

not attested not anchored not stored refs pending

Criteria for Morin singularities for maps into lower dimensions, and applications

Kentaro Saji

arxiv:1510.05537 v2 · 2015-10-19 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VIVIOXFTZGKI7BW4CSQPQANN22}

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	2026-05-18T01:29:37.851968Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aa2a875cb3c9948f86dc14a0f801add68f8c7400f58b1c5977d045ae574aec09

Aliases

arxiv: 1510.05537 · arxiv_version: 1510.05537v2 · doi: 10.48550/arxiv.1510.05537 · pith_short_12: VIVIOXFTZGKI · pith_short_16: VIVIOXFTZGKI7BW4 · pith_short_8: VIVIOXFT

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/VIVIOXFTZGKI7BW4CSQPQANN22 \
  | 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: aa2a875cb3c9948f86dc14a0f801add68f8c7400f58b1c5977d045ae574aec09

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1aaa6025136db876364c2b789c6de66eeb79487bddd14808d06d04b2744f9232",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2015-10-19T15:43:04Z",
    "title_canon_sha256": "cf46d28045e03b4fb05914e995ae095dd56a77a11a433c611f54c40cb1bb58e6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.05537",
    "kind": "arxiv",
    "version": 2
  }
}