Pith Number

pith:6P55335X

pith:2015:6P55335X55VFWRKFIWZZWBWSVD

not attested not anchored not stored refs pending

The Upsilon function of L-space knots is a Legendre transform

Maciej Borodzik, Matthew Hedden

arxiv:1505.06672 v2 · 2015-05-25 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6P55335X55VFWRKFIWZZWBWSVD}

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	2026-05-18T01:39:54.727583Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f3fbddefb7ef6a5b454545b39b06d2a8c8289c0b7257f8087164b96767bce730

Aliases

arxiv: 1505.06672 · arxiv_version: 1505.06672v2 · doi: 10.48550/arxiv.1505.06672 · pith_short_12: 6P55335X55VF · pith_short_16: 6P55335X55VFWRKF · pith_short_8: 6P55335X

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/6P55335X55VFWRKFIWZZWBWSVD \
  | 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: f3fbddefb7ef6a5b454545b39b06d2a8c8289c0b7257f8087164b96767bce730

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "245a76f88503ea1bc6b71dc20e5ed6a8ff96d0078a50e5579ec1057d95d42d84",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2015-05-25T15:54:18Z",
    "title_canon_sha256": "e49c6aa1f3418da0f96458b77949a5ebd20a6a5529c758008539e9926f656ea3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.06672",
    "kind": "arxiv",
    "version": 2
  }
}