Pith Number

pith:Z5K6RFW6

pith:2018:Z5K6RFW6M3B25LKMWFDSN6ZS5N

not attested not anchored not stored refs pending

Mountain pass energies between homotopy classes of maps

Daniel Stern

arxiv:1809.03361 v1 · 2018-09-10 · math.DG · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Z5K6RFW6M3B25LKMWFDSN6ZS5N}

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	2026-05-18T00:06:07.091301Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cf55e896de66c3aead4cb14726fb32eb64cb0d84a211fc2efb531ca088e8f223

Aliases

arxiv: 1809.03361 · arxiv_version: 1809.03361v1 · doi: 10.48550/arxiv.1809.03361 · pith_short_12: Z5K6RFW6M3B2 · pith_short_16: Z5K6RFW6M3B25LKM · pith_short_8: Z5K6RFW6

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/Z5K6RFW6M3B25LKMWFDSN6ZS5N \
  | 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: cf55e896de66c3aead4cb14726fb32eb64cb0d84a211fc2efb531ca088e8f223

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9183a4d3d405ea7aa5b9e17b9f60819d7117100a28adee21a22c54ab3c8f958d",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2018-09-10T14:43:03Z",
    "title_canon_sha256": "709ca5694bb4bc1d826efa5494a8a1ecddc9d8d265ea0d780d12047bff391ae1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1809.03361",
    "kind": "arxiv",
    "version": 1
  }
}