Pith Number

pith:3NKUGY2L

pith:2017:3NKUGY2LB54WSXL5FTICYLRB2D

not attested not anchored not stored refs pending

Precise estimates for biorthogonal families under asymptotic gap conditions

Judith Vancostenoble, Patrick Martinez, Piermarco Cannarsa

arxiv:1706.02435 v1 · 2017-06-08 · math.OC · 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{3NKUGY2LB54WSXL5FTICYLRB2D}

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	2026-05-18T00:42:45.453916Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

db5543634b0f79695d7d2cd02c2e21d0fbfd0117dad9e66d103b8aa989c51ed9

Aliases

arxiv: 1706.02435 · arxiv_version: 1706.02435v1 · doi: 10.48550/arxiv.1706.02435 · pith_short_12: 3NKUGY2LB54W · pith_short_16: 3NKUGY2LB54WSXL5 · pith_short_8: 3NKUGY2L

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/3NKUGY2LB54WSXL5FTICYLRB2D \
  | 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: db5543634b0f79695d7d2cd02c2e21d0fbfd0117dad9e66d103b8aa989c51ed9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3accb6147066bb2c7f91a25710ea02d60b09d6e560fd75ff9427f8621b351fe9",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2017-06-08T02:45:33Z",
    "title_canon_sha256": "f6404f492a97701f957acddac60e4be4620e84d11bc7471a3ca1497e1c1ce507"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1706.02435",
    "kind": "arxiv",
    "version": 1
  }
}