Pith Number

pith:OPLPG3QN

pith:2020:OPLPG3QNOO7TTK6XFW7YP5ZZ47

not attested not anchored not stored refs pending

Linear turnpike theorem

CaGE ), Emmanuel Tr\'elat (LJLL

arxiv:2010.13605 v3 · 2020-10-26 · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OPLPG3QNOO7TTK6XFW7YP5ZZ47}

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	2026-07-05T05:31:38.512994Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

73d6f36e0d73bf39abd72dbf87f739e7d72828336980ab62dae49cb5828b51ea

Aliases

arxiv: 2010.13605 · arxiv_version: 2010.13605v3 · doi: 10.48550/arxiv.2010.13605 · pith_short_12: OPLPG3QNOO7T · pith_short_16: OPLPG3QNOO7TTK6X · pith_short_8: OPLPG3QN

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/OPLPG3QNOO7TTK6XFW7YP5ZZ47 \
  | 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: 73d6f36e0d73bf39abd72dbf87f739e7d72828336980ab62dae49cb5828b51ea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "512c080672cd8360fa4f4850d20d6302eda85479da20e7a09db3b06ef7aab891",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2020-10-26T14:20:58Z",
    "title_canon_sha256": "f4c556a2ee8f08acfbfce5fb83072df2c3c0387275f275c5b0defc016a155f5d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2010.13605",
    "kind": "arxiv",
    "version": 3
  }
}