Pith Number

pith:DTJ7YTRC

pith:2015:DTJ7YTRC23TGMBNVREA6BIPZCD

not attested not anchored not stored refs pending

Duality for increasing convex functionals with countably many marginal constraints

Daniel Bartl, Ludovic Tangpi, Michael Kupper, Patrick Cheridito

arxiv:1509.08988 v2 · 2015-09-30 · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DTJ7YTRC23TGMBNVREA6BIPZCD}

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	2026-05-18T00:50:22.902850Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1cd3fc4e22d6e66605b58901e0a1f910cc4b1a7c1ecb4d818981225de4a7cb42

Aliases

arxiv: 1509.08988 · arxiv_version: 1509.08988v2 · doi: 10.48550/arxiv.1509.08988 · pith_short_12: DTJ7YTRC23TG · pith_short_16: DTJ7YTRC23TGMBNV · pith_short_8: DTJ7YTRC

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/DTJ7YTRC23TGMBNVREA6BIPZCD \
  | 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: 1cd3fc4e22d6e66605b58901e0a1f910cc4b1a7c1ecb4d818981225de4a7cb42

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9aee4dd9155fad95bacc7856f5ea297c5e337ccc39943e2a3c5b9e0c37999eaa",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2015-09-30T01:27:27Z",
    "title_canon_sha256": "a02b63701801adbf54cb993403a31f69dfcd9b5f163100ac033fccbbb8b7d294"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.08988",
    "kind": "arxiv",
    "version": 2
  }
}