Pith Number

pith:QVSO5GIS

pith:2016:QVSO5GISFPRXBGYNI4TZ5WDHPS

not attested not anchored not stored refs pending

The Morse-Bott inequalities, orientations, and the Thom isomorphism in Morse homology

Thomas O. Rot

arxiv:1607.06244 v1 · 2016-07-21 · math.GT · math.AT · math.SG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QVSO5GISFPRXBGYNI4TZ5WDHPS}

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	2026-05-18T01:10:42.173829Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8564ee99122be3709b0d47279ed8677c80d606fcff4451ad465d171fae4c39c0

Aliases

arxiv: 1607.06244 · arxiv_version: 1607.06244v1 · doi: 10.48550/arxiv.1607.06244 · pith_short_12: QVSO5GISFPRX · pith_short_16: QVSO5GISFPRXBGYN · pith_short_8: QVSO5GIS

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/QVSO5GISFPRXBGYNI4TZ5WDHPS \
  | 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: 8564ee99122be3709b0d47279ed8677c80d606fcff4451ad465d171fae4c39c0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "78e1aa09667593c3bcab911cbbab573b280aab18ab5e68b718c1c063f6bb5fd0",
    "cross_cats_sorted": [
      "math.AT",
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2016-07-21T09:25:31Z",
    "title_canon_sha256": "33697ecbc77490b2b5db14493dbe81b204e83f75e055ba0bc875c9d63f620fc7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.06244",
    "kind": "arxiv",
    "version": 1
  }
}