Pith Number

pith:XRTACGRO

pith:2014:XRTACGROOIYXEUMSTDJUP6QRZG

not attested not anchored not stored refs pending

Morse's index formula in VMO for compact manifolds with boundary

Antonio Segatti, Giacomo Canevari, Marco Veneroni

arxiv:1407.1707 v2 · 2014-07-07 · math.FA · 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{XRTACGROOIYXEUMSTDJUP6QRZG}

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	2026-05-18T01:33:57.028530Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bc66011a2e723172519298d347fa11c989ff375cccd42fbea77c44e92216877a

Aliases

arxiv: 1407.1707 · arxiv_version: 1407.1707v2 · doi: 10.48550/arxiv.1407.1707 · pith_short_12: XRTACGROOIYX · pith_short_16: XRTACGROOIYXEUMS · pith_short_8: XRTACGRO

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/XRTACGROOIYXEUMSTDJUP6QRZG \
  | 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: bc66011a2e723172519298d347fa11c989ff375cccd42fbea77c44e92216877a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0e79977391821baf5d0d8d6265420cdef1a392d6f72de91c4721cfe1f11bbce2",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2014-07-07T13:29:17Z",
    "title_canon_sha256": "d9c918e26e27b7a1e4647d56a2b2c995d20324e7a25416b009910ab9beb1e1f8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1407.1707",
    "kind": "arxiv",
    "version": 2
  }
}