Pith Number

pith:MSE4O6QO

pith:2017:MSE4O6QOBAXDQKCM5NALUBE2IV

not attested not anchored not stored refs pending

Chord Shortening Flow and a Theorem of Lusternik and Schnirelmann

Martin Li

arxiv:1707.04014 v1 · 2017-07-13 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MSE4O6QOBAXDQKCM5NALUBE2IV}

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	2026-05-17T23:44:15.689398Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6489c77a0e082e38284ceb40ba049a45552e45e4aa92dfb25a2cff0836297258

Aliases

arxiv: 1707.04014 · arxiv_version: 1707.04014v1 · doi: 10.48550/arxiv.1707.04014 · pith_short_12: MSE4O6QOBAXD · pith_short_16: MSE4O6QOBAXDQKCM · pith_short_8: MSE4O6QO

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/MSE4O6QOBAXDQKCM5NALUBE2IV \
  | 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: 6489c77a0e082e38284ceb40ba049a45552e45e4aa92dfb25a2cff0836297258

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3d6da93fa2f91c40c02dfbf0fda1f93ab284914b39f9b63308cecafb7fcfd147",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2017-07-13T07:49:27Z",
    "title_canon_sha256": "ba18f8a583b898d2cad3ac3b3a09ba94b612614464da9e0fe24f6539a448410f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1707.04014",
    "kind": "arxiv",
    "version": 1
  }
}