Pith Number

pith:QV6VJNWF

pith:2016:QV6VJNWFL6RLFSEUQBC3SDI4ND

not attested not anchored not stored refs pending

Fatou's Lemma, Galerkin Approximations and the Existence of Walrasian Equilibria in Infinite Dimensions

M. Ali Khan, Nobusumi Sagara

arxiv:1610.04776 v2 · 2016-10-15 · 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{QV6VJNWFL6RLFSEUQBC3SDI4ND}

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	2026-05-18T00:50:29.056583Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

857d54b6c55fa2b2c8948045b90d1c68cb4b223d8e1c4d8d14722e459948cc29

Aliases

arxiv: 1610.04776 · arxiv_version: 1610.04776v2 · doi: 10.48550/arxiv.1610.04776 · pith_short_12: QV6VJNWFL6RL · pith_short_16: QV6VJNWFL6RLFSEU · pith_short_8: QV6VJNWF

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/QV6VJNWFL6RLFSEUQBC3SDI4ND \
  | 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: 857d54b6c55fa2b2c8948045b90d1c68cb4b223d8e1c4d8d14722e459948cc29

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "015b4c1953d86a0fb68cd64cb78cb80f2c20ffa77ffb5be6fa35f016bab77870",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2016-10-15T19:31:12Z",
    "title_canon_sha256": "b1ff4607922a515750b952f7321f5906c46aa705d33bb433296b2d81b8095595"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.04776",
    "kind": "arxiv",
    "version": 2
  }
}