Pith Number

pith:AE3XKPEX

pith:2012:AE3XKPEXSXJHO4X4M6AAVBVTVH

not attested not anchored not stored refs pending

Existence of optima and equilibria for traffic flow on networks

Alberto Bressan, Ke Han

arxiv:1211.1355 v2 · 2012-11-06 · 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{AE3XKPEXSXJHO4X4M6AAVBVTVH}

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	2026-05-18T01:18:18.647613Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0137753c9795d27772fc67800a86b3a9f54b1b804a78e2cc1d5391ff352c5768

Aliases

arxiv: 1211.1355 · arxiv_version: 1211.1355v2 · doi: 10.48550/arxiv.1211.1355 · pith_short_12: AE3XKPEXSXJH · pith_short_16: AE3XKPEXSXJHO4X4 · pith_short_8: AE3XKPEX

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/AE3XKPEXSXJHO4X4M6AAVBVTVH \
  | 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: 0137753c9795d27772fc67800a86b3a9f54b1b804a78e2cc1d5391ff352c5768

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "97e25ccba936d59381a8047ed5718623008f6099441e2c48e174bae2356f385c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-11-06T19:30:18Z",
    "title_canon_sha256": "ecae5cd95078b084124c037565115e52f9176f2d04354b5abbf1044384e5f274"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.1355",
    "kind": "arxiv",
    "version": 2
  }
}