Pith Number

pith:FDMNVY2N

pith:2026:FDMNVY2NQ6YOIF4RVKQO5PR4W3

not attested not anchored not stored refs resolved

How Far Back in Time a Digital Twin Reflects the State of the Physical Object: Age of Staleness

Ismail Cosandal, Sennur Ulukus

Age of staleness measures the time since a remote estimate of a Markov source last matched the true state.

arxiv:2605.16176 v1 · 2026-05-15 · cs.IT · cs.NI · eess.SP · math.IT

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\usepackage{pith}
\pithnumber{FDMNVY2NQ6YOIF4RVKQO5PR4W3}

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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.

Claims

C1strongest claim

We introduce a novel metric coined age of staleness (AoS) that measures when the last time that the current estimation was correct.

C2weakest assumption

The physical objects are modeled as n-ary symmetric Markov sources observed via constant-rate sampling (abstract, first analysis paragraph).

C3one line summary

Introduces age of staleness (AoS) metric for remote estimation of Markov sources and optimizes sampling rate allocation under total rate constraint for digital twin networks.

References

31 extracted · 31 resolved · 0 Pith anchors

[1] Real-time status: How often should one update? 2012

[2] Age of information: An introduction and survey, 2021

[3] Age of information in gossip networks: A friendly introduction and literature survey invited paper, 2025

[4] Age of information in internet of things: A survey, 2023

[5] The age of incorrect information: A new performance metric for status updates, 2020

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:01:56.282998Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

28d8dae34d87b0e41791aaa0eebe3cb6cd1cdf68d53fd2d8ac577a70827ce58f

Aliases

arxiv: 2605.16176 · arxiv_version: 2605.16176v1 · doi: 10.48550/arxiv.2605.16176 · pith_short_12: FDMNVY2NQ6YO · pith_short_16: FDMNVY2NQ6YOIF4R · pith_short_8: FDMNVY2N

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/FDMNVY2NQ6YOIF4RVKQO5PR4W3 \
  | 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: 28d8dae34d87b0e41791aaa0eebe3cb6cd1cdf68d53fd2d8ac577a70827ce58f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0caefd65d9a17ff4d1534ceeabcc7fc086163614dea6e834a8049bb3b418b3f4",
    "cross_cats_sorted": [
      "cs.NI",
      "eess.SP",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2026-05-15T16:55:00Z",
    "title_canon_sha256": "d62d6a1ee346ad0e0df047df2077f856b59df66d1ec3b1bff01c1affd5fd2daa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16176",
    "kind": "arxiv",
    "version": 1
  }
}