Paper Citation Record · LEDGER

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems

As of 14 August 2026, this Paper Citation Record lists 46 of 46 outbound references and 1 inbound Pith citation observation for arXiv:2606.04816.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2606.04816 v1

Coverage vector

measured 46 of 46 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-28T05:51:28.335337Z

measured 47 of 47 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-01T20:26:11.175716Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

46 of 46 outbound references displayed

verified exact1
verified fuzzy0
unresolved44
parse uncertain0
malformed identifier0
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 1a6dedbd-2825-498e-ab5a-ad295c2128be · outbound

This paper cites Proximal Policy Optimization Algorithms.

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems Proximal Policy Optimization Algorithms

Reference 1

Resolution: verified exact; local_arxiv, observed 2026-07-02T08:36:48.628673Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 01a0f7ab-165b-4f85-9f1b-79ff1d7db505 · outbound

This paper cites arXiv preprint arXiv:2509.22979 (2025).

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems arXiv preprint arXiv:2509.22979 (2025)

Reference 2

Resolution: metadata mismatch; arxiv_id, observed 2026-07-02T08:36:48.631792Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation cc99f921-dde5-4905-8a04-de0d93c81d9a · outbound

This paper cites an unresolved cited work.

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems Unresolved cited work

Reference 3

Resolution: unresolved; no resolver link, observed 2026-06-28T05:51:28.335337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 876c0fbb-6525-45c0-b864-c09b23caf5fc · outbound

This paper cites Frontier ﬁltering.

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems Frontier ﬁltering

Reference 4

Resolution: unresolved; no resolver link, observed 2026-06-28T05:51:28.335337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 67fb63c0-3c60-4449-839d-b4c26ffb412b · outbound

This paper cites Do not omit, invent, or round any number.

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems Do not omit, invent, or round any number

Reference 5

Resolution: unresolved; no resolver link, observed 2026-06-28T05:51:28.335337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c7723136-f140-4d3f-a047-b49887eac3c4 · outbound

This paper cites No math symbols, variable names, or code jargon.

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems No math symbols, variable names, or code jargon

Reference 6

Resolution: unresolved; no resolver link, observed 2026-06-28T05:51:28.335337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 41acaf8a-1962-478c-878a-143f8430971d · outbound

This paper cites Truck 0 (capacity 50.0, ﬁxed cost 70.0).

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems Truck 0 (capacity 50.0, ﬁxed cost 70.0)

Reference 7

Resolution: unresolved; no resolver link, observed 2026-06-28T05:51:28.335337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c54b3259-7787-46eb-a11d-6dcf89f42efb · outbound

This paper cites 3.4 pallets.

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems 3.4 pallets

Reference 8

Resolution: unresolved; no resolver link, observed 2026-06-28T05:51:28.335337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 21591e79-cebf-43a4-9684-3b3b6c8f1ee2 · outbound

This paper cites Use a tangible goods unit instead.

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems Use a tangible goods unit instead

Reference 9

Resolution: unresolved; no resolver link, observed 2026-06-28T05:51:28.335337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7149953d-6593-40dc-be6b-fe61012f9e06 · outbound

This paper cites an unresolved cited work.

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems Unresolved cited work

Reference 10

Resolution: unresolved; no resolver link, observed 2026-06-28T05:51:28.335337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fc81984e-a6c8-4025-b5c6-dd5b9dacf533 · outbound

This paper cites No Markdown, no bullets/tables/dialogue/email tone.

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems No Markdown, no bullets/tables/dialogue/email tone

Reference 11

Resolution: unresolved; no resolver link, observed 2026-06-28T05:51:28.335337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 88af0722-918c-491c-9544-ef329d6724e8 · outbound

This paper cites a capacity of 50.0.

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems a capacity of 50.0

Reference 12

Resolution: unresolved; no resolver link, observed 2026-06-28T05:51:28.335337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 48eb12e7-6229-4f73-a488-1eed96d72927 · outbound

This paper cites an unresolved cited work.

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems Unresolved cited work

Reference 13

Resolution: unresolved; no resolver link, observed 2026-06-28T05:51:28.335337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7aba5ab1-c73a-464a-b581-22e233756cb7 · outbound

This paper cites an unresolved cited work.

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems Unresolved cited work

Reference 14

Resolution: unresolved; no resolver link, observed 2026-06-28T05:51:28.335337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ef358849-e280-46e4-ac9b-56decf20a6d4 · outbound

This paper cites an unresolved cited work.

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems Unresolved cited work

Reference 15

Resolution: unresolved; no resolver link, observed 2026-06-28T05:51:28.335337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 47dac5bc-92d7-466f-abdc-b9beb94e2585 · outbound

This paper cites an unresolved cited work.

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems Unresolved cited work

Reference 16

Resolution: unresolved; no resolver link, observed 2026-06-28T05:51:28.335337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c4d751a6-0a97-40b1-85ed-21d49265763e · outbound

This paper cites an unresolved cited work.

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems Unresolved cited work

Reference 17

Resolution: unresolved; no resolver link, observed 2026-06-28T05:51:28.335337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 38e0bdcc-1a85-41b3-9f0d-7e0390cd02fe · outbound

This paper cites an unresolved cited work.

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems Unresolved cited work

Reference 18

Resolution: unresolved; no resolver link, observed 2026-06-28T05:51:28.335337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cde8a363-d341-4c69-bac9-c6928f75d389 · outbound

This paper cites an unresolved cited work.

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems Unresolved cited work

Reference 19

Resolution: unresolved; no resolver link, observed 2026-06-28T05:51:28.335337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 84b5c156-e9ea-435a-9ac7-c38fc0bc181e · outbound

This paper cites an unresolved cited work.

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems Unresolved cited work

Reference 20

Resolution: unresolved; no resolver link, observed 2026-06-28T05:51:28.335337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fcde5fa7-2911-4c4a-ac3a-7530f67591de · outbound

This paper cites an unresolved cited work.

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-06-28T05:51:28.335337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 03308eaf-935e-4dfc-8fcf-e976866fed10 · outbound

This paper cites an unresolved cited work.

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems Unresolved cited work

Reference 22

Resolution: unresolved; no resolver link, observed 2026-06-28T05:51:28.335337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9f1ab420-b5e1-4722-8e42-e38763dfb11d · outbound

This paper cites Do not delete, alter, round, merge, or restate numbers in a different form.

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems Do not delete, alter, round, merge, or restate numbers in a different form

Reference 23

Resolution: unresolved; no resolver link, observed 2026-06-28T05:51:28.335337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4072618d-a5f1-429f-b211-8d2553b2f679 · outbound

This paper cites Do not renumber, reorder, relabel, or collapse depots, customers, vehicles, compartments, pickup−delivery pairs, or any other named entities.

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems Do not renumber, reorder, relabel, or collapse depots, customers, vehicles, compartments, pickup−delivery pairs, or any other named entities

Reference 24

Resolution: unresolved; no resolver link, observed 2026-06-28T05:51:28.335337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 15ecd0f9-2116-4587-adbb-9681f33dc9fd · outbound

This paper cites an unresolved cited work.

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems Unresolved cited work

Reference 25

Resolution: unresolved; no resolver link, observed 2026-06-28T05:51:28.335337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4aeeb63f-7c0b-4354-925b-d45fc739c895 · outbound

This paper cites This is condensation, not stylistic rewriting.

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems This is condensation, not stylistic rewriting

Reference 26

Resolution: unresolved; no resolver link, observed 2026-06-28T05:51:28.335337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b582674b-7396-4d88-91d0-98d367910aff · outbound

This paper cites an unresolved cited work.

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems Unresolved cited work

Reference 27

Resolution: unresolved; no resolver link, observed 2026-06-28T05:51:28.335337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 33a507d4-4596-4be0-a31d-d0a1163c99c1 · outbound

This paper cites each node has exactly one incoming arc and exactly one outgoing arc.

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems each node has exactly one incoming arc and exactly one outgoing arc

Reference 28

Resolution: unresolved; no resolver link, observed 2026-06-28T05:51:28.335337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1f69f7ae-8738-4d8d-b116-832f924fc8db · outbound

This paper cites Remove tutorial tone, repeated reminders, and repeated restatements of the same requirement.

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems Remove tutorial tone, repeated reminders, and repeated restatements of the same requirement

Reference 29

Resolution: unresolved; no resolver link, observed 2026-06-28T05:51:28.335337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ec45706e-7548-4830-9bda-145a94a5c3a2 · outbound

This paper cites Do not output bullets, markdown, JSON, XML, commentary, or surrounding quotation marks.

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems Do not output bullets, markdown, JSON, XML, commentary, or surrounding quotation marks

Reference 30

Resolution: unresolved; no resolver link, observed 2026-06-28T05:51:28.335337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 483d08c6-e45c-4878-a16c-bd368f8cf5a4 · outbound

This paper cites Output only the condensed problem statement.

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems Output only the condensed problem statement

Reference 31

Resolution: unresolved; no resolver link, observed 2026-06-28T05:51:28.335337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bfceef29-998f-4fc5-955d-e18186a82a77 · outbound

This paper cites no arcs into the start depot.

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems no arcs into the start depot

Reference 32

Resolution: unresolved; no resolver link, observed 2026-06-28T05:51:28.335337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c49c6a9a-8b43-4162-aac5-cc0983ad847e · outbound

This paper cites virtual depot.

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems virtual depot

Reference 33

Resolution: unresolved; no resolver link, observed 2026-06-28T05:51:28.335337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a4ca375d-e4b9-448b-b16c-1e8f8f94a2af · outbound

This paper cites an unresolved cited work.

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems Unresolved cited work

Reference 34

Resolution: unresolved; no resolver link, observed 2026-06-28T05:51:28.335337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 145f235e-e2f8-4b25-9117-03c0ad375517 · outbound

This paper cites an unresolved cited work.

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems Unresolved cited work

Reference 35

Resolution: unresolved; no resolver link, observed 2026-06-28T05:51:28.335337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b76ed50e-1ede-4467-b1af-1168f8cc6e5f · outbound

This paper cites Do not rely on any external mapping table.

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems Do not rely on any external mapping table

Reference 36

Resolution: unresolved; no resolver link, observed 2026-06-28T05:51:28.335337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 27573af8-bc06-4ce0-a5d8-5cc3cc0a660e · outbound

This paper cites an unresolved cited work.

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems Unresolved cited work

Reference 37

Resolution: unresolved; no resolver link, observed 2026-06-28T05:51:28.335337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6899062c-f355-420f-a5e9-f9b7793fee80 · outbound

This paper cites an unresolved cited work.

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems Unresolved cited work

Reference 38

Resolution: unresolved; no resolver link, observed 2026-06-28T05:51:28.335337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 13317cf8-b4be-4493-824b-f2875c664098 · outbound

This paper cites an unresolved cited work.

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems Unresolved cited work

Reference 39

Resolution: unresolved; no resolver link, observed 2026-06-28T05:51:28.335337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b33f0467-2c6a-4174-b669-b67e05de4759 · outbound

This paper cites an unresolved cited work.

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems Unresolved cited work

Reference 40

Resolution: unresolved; no resolver link, observed 2026-06-28T05:51:28.335337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 259f1885-b684-483f-bd04-815e4368d285 · outbound

This paper cites rewritten_nl.

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems rewritten_nl

Reference 41

Resolution: unresolved; no resolver link, observed 2026-06-28T05:51:28.335337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e73e599d-6bd3-4e5d-ad26-70302d99229a · outbound

This paper cites an unresolved cited work.

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems Unresolved cited work

Reference 42

Resolution: unresolved; no resolver link, observed 2026-06-28T05:51:28.335337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c8f13e03-c416-410c-939e-7fec538a257f · outbound

This paper cites It must call m.optimize() and return the model object.

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems It must call m.optimize() and return the model object

Reference 43

Resolution: unresolved; no resolver link, observed 2026-06-28T05:51:28.335337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0197a0f1-0414-4f55-ad14-8ee371b9195f · outbound

This paper cites an unresolved cited work.

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems Unresolved cited work

Reference 44

Resolution: unresolved; no resolver link, observed 2026-06-28T05:51:28.335337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d6d11a9f-b667-406b-8d0d-293b72576a93 · outbound

This paper cites an unresolved cited work.

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems Unresolved cited work

Reference 45

Resolution: unresolved; no resolver link, observed 2026-06-28T05:51:28.335337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7ea385da-8772-4563-b760-2cf81c8d9d64 · outbound

This paper cites an unresolved cited work.

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems Unresolved cited work

Reference 46

Resolution: unresolved; no resolver link, observed 2026-06-28T05:51:28.335337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation dde9e2c0-a1fc-4c5c-b4c1-0cabe855abed · inbound

Falsification-Based Verification of LLM-Generated Optimization Models: Sound Test Batteries and Their Detection Limits cites this paper.

Falsification-Based Verification of LLM-Generated Optimization Models: Sound Test Batteries and Their Detection Limits Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-01T20:26:11.175716Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.