Pith Number

pith:FKMOZRJZ

pith:2011:FKMOZRJZ6V47OK2PMDVUV5UVM4

not attested not anchored not stored refs pending

The minimal Morse components of translations on flag manifolds are normally hyperbolic

Lucas Seco, Mauro Patr\~ao

arxiv:1110.4915 v2 · 2011-10-21 · 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{FKMOZRJZ6V47OK2PMDVUV5UVM4}

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	2026-05-18T01:15:32.826624Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2a98ecc539f579f72b4f60eb4af6956726a1a4b6d7999ebee33bdc26e51a5da0

Aliases

arxiv: 1110.4915 · arxiv_version: 1110.4915v2 · doi: 10.48550/arxiv.1110.4915 · pith_short_12: FKMOZRJZ6V47 · pith_short_16: FKMOZRJZ6V47OK2P · pith_short_8: FKMOZRJZ

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/FKMOZRJZ6V47OK2PMDVUV5UVM4 \
  | 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: 2a98ecc539f579f72b4f60eb4af6956726a1a4b6d7999ebee33bdc26e51a5da0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "77d070f5d59caa856160f81359d61effa596efc02ae778e3e9be991d8859b167",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-10-21T21:47:55Z",
    "title_canon_sha256": "d84223d10f2ac2d644f9da2e682696b42eac9ea11a68bbd33aef13f69337c8a9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.4915",
    "kind": "arxiv",
    "version": 2
  }
}