{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:OOSEXEBS6DCKV5ESHYJL2QQZJY","short_pith_number":"pith:OOSEXEBS","canonical_record":{"source":{"id":"2606.06353","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-04T16:22:44Z","cross_cats_sorted":[],"title_canon_sha256":"3311dfc3403925e1ecdd59a537d0ff1952e727089efb8b8a65f00c23dc3f5521","abstract_canon_sha256":"ca60dd7aef75a14c7cc89c1c4eb17803f9fe232c72e36d6cb7cbd157e12e1fc1"},"schema_version":"1.0"},"canonical_sha256":"73a44b9032f0c4aaf4923e12bd42194e14726eef2a5ded7914212390c0ff82a7","source":{"kind":"arxiv","id":"2606.06353","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.06353","created_at":"2026-06-05T01:15:42Z"},{"alias_kind":"arxiv_version","alias_value":"2606.06353v1","created_at":"2026-06-05T01:15:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.06353","created_at":"2026-06-05T01:15:42Z"},{"alias_kind":"pith_short_12","alias_value":"OOSEXEBS6DCK","created_at":"2026-06-05T01:15:42Z"},{"alias_kind":"pith_short_16","alias_value":"OOSEXEBS6DCKV5ES","created_at":"2026-06-05T01:15:42Z"},{"alias_kind":"pith_short_8","alias_value":"OOSEXEBS","created_at":"2026-06-05T01:15:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:OOSEXEBS6DCKV5ESHYJL2QQZJY","target":"record","payload":{"canonical_record":{"source":{"id":"2606.06353","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-04T16:22:44Z","cross_cats_sorted":[],"title_canon_sha256":"3311dfc3403925e1ecdd59a537d0ff1952e727089efb8b8a65f00c23dc3f5521","abstract_canon_sha256":"ca60dd7aef75a14c7cc89c1c4eb17803f9fe232c72e36d6cb7cbd157e12e1fc1"},"schema_version":"1.0"},"canonical_sha256":"73a44b9032f0c4aaf4923e12bd42194e14726eef2a5ded7914212390c0ff82a7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-05T01:15:42.542300Z","signature_b64":"2yCUwkGv2BDFp406PrBslSywYehW88YY2EiOdZtp6yfrhDRf9d06jRLVjf5Pqi8v1uVuacUZ6EGPVBvLv6TRAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"73a44b9032f0c4aaf4923e12bd42194e14726eef2a5ded7914212390c0ff82a7","last_reissued_at":"2026-06-05T01:15:42.541894Z","signature_status":"signed_v1","first_computed_at":"2026-06-05T01:15:42.541894Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.06353","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-05T01:15:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yEJ9IjhVUOddXWFLOYwWZGVEvARkiNb5oYmppou9j6PnWh4S/DLqASfCYSraIherqxcwMzLezyhixkb+EXPXDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T18:31:23.664575Z"},"content_sha256":"36b30d0a334af26d4e85cce7a948983912fa31db447d28a4905057f846afaad9","schema_version":"1.0","event_id":"sha256:36b30d0a334af26d4e85cce7a948983912fa31db447d28a4905057f846afaad9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:OOSEXEBS6DCKV5ESHYJL2QQZJY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Maximising the Set-Piece Return: Optimising Football Corner Tactics with Graph Reinforcement Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Axl Rice, Francisco Belo, Liam Anderson, Michael Groom, Sean Groom, Shuo Wang, Victor-Alexandru Darvariu","submitted_at":"2026-06-04T16:22:44Z","abstract_excerpt":"Machine learning is increasingly employed for the evaluation of football tactics. However, existing approaches focus on characterising historical actions or analyst-specified counterfactual scenarios. In this work, we seek to go beyond the imitation of historically observed patterns towards discovering new generalisable player configurations and strategies. To tackle this, we focus on optimising corner kick routines, and formulate a decision-making problem in which a central policy makes adjustments to attacking player positions and velocities to maximise first contact shot probability. Unlike"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06353","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.06353/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-05T01:15:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"unvP5tf//2XztT/RRrHfbpVvZOM0DnYj9oS/BIhzzF2u8pXWSfDmZa4KZiivCZAFdJkN79SIlLWei3IgV2tsCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T18:31:23.664940Z"},"content_sha256":"e355a8e5aa31f4d598247352dd8f46997c3ff45fff723b8febfa533ddc5e6b72","schema_version":"1.0","event_id":"sha256:e355a8e5aa31f4d598247352dd8f46997c3ff45fff723b8febfa533ddc5e6b72"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OOSEXEBS6DCKV5ESHYJL2QQZJY/bundle.json","state_url":"https://pith.science/pith/OOSEXEBS6DCKV5ESHYJL2QQZJY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OOSEXEBS6DCKV5ESHYJL2QQZJY/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-25T18:31:23Z","links":{"resolver":"https://pith.science/pith/OOSEXEBS6DCKV5ESHYJL2QQZJY","bundle":"https://pith.science/pith/OOSEXEBS6DCKV5ESHYJL2QQZJY/bundle.json","state":"https://pith.science/pith/OOSEXEBS6DCKV5ESHYJL2QQZJY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OOSEXEBS6DCKV5ESHYJL2QQZJY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:OOSEXEBS6DCKV5ESHYJL2QQZJY","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"ca60dd7aef75a14c7cc89c1c4eb17803f9fe232c72e36d6cb7cbd157e12e1fc1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-04T16:22:44Z","title_canon_sha256":"3311dfc3403925e1ecdd59a537d0ff1952e727089efb8b8a65f00c23dc3f5521"},"schema_version":"1.0","source":{"id":"2606.06353","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.06353","created_at":"2026-06-05T01:15:42Z"},{"alias_kind":"arxiv_version","alias_value":"2606.06353v1","created_at":"2026-06-05T01:15:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.06353","created_at":"2026-06-05T01:15:42Z"},{"alias_kind":"pith_short_12","alias_value":"OOSEXEBS6DCK","created_at":"2026-06-05T01:15:42Z"},{"alias_kind":"pith_short_16","alias_value":"OOSEXEBS6DCKV5ES","created_at":"2026-06-05T01:15:42Z"},{"alias_kind":"pith_short_8","alias_value":"OOSEXEBS","created_at":"2026-06-05T01:15:42Z"}],"graph_snapshots":[{"event_id":"sha256:e355a8e5aa31f4d598247352dd8f46997c3ff45fff723b8febfa533ddc5e6b72","target":"graph","created_at":"2026-06-05T01:15:42Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.06353/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Machine learning is increasingly employed for the evaluation of football tactics. However, existing approaches focus on characterising historical actions or analyst-specified counterfactual scenarios. In this work, we seek to go beyond the imitation of historically observed patterns towards discovering new generalisable player configurations and strategies. To tackle this, we focus on optimising corner kick routines, and formulate a decision-making problem in which a central policy makes adjustments to attacking player positions and velocities to maximise first contact shot probability. Unlike","authors_text":"Axl Rice, Francisco Belo, Liam Anderson, Michael Groom, Sean Groom, Shuo Wang, Victor-Alexandru Darvariu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-04T16:22:44Z","title":"Maximising the Set-Piece Return: Optimising Football Corner Tactics with Graph Reinforcement Learning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06353","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:36b30d0a334af26d4e85cce7a948983912fa31db447d28a4905057f846afaad9","target":"record","created_at":"2026-06-05T01:15:42Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"ca60dd7aef75a14c7cc89c1c4eb17803f9fe232c72e36d6cb7cbd157e12e1fc1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-04T16:22:44Z","title_canon_sha256":"3311dfc3403925e1ecdd59a537d0ff1952e727089efb8b8a65f00c23dc3f5521"},"schema_version":"1.0","source":{"id":"2606.06353","kind":"arxiv","version":1}},"canonical_sha256":"73a44b9032f0c4aaf4923e12bd42194e14726eef2a5ded7914212390c0ff82a7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"73a44b9032f0c4aaf4923e12bd42194e14726eef2a5ded7914212390c0ff82a7","first_computed_at":"2026-06-05T01:15:42.541894Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-05T01:15:42.541894Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2yCUwkGv2BDFp406PrBslSywYehW88YY2EiOdZtp6yfrhDRf9d06jRLVjf5Pqi8v1uVuacUZ6EGPVBvLv6TRAw==","signature_status":"signed_v1","signed_at":"2026-06-05T01:15:42.542300Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.06353","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:36b30d0a334af26d4e85cce7a948983912fa31db447d28a4905057f846afaad9","sha256:e355a8e5aa31f4d598247352dd8f46997c3ff45fff723b8febfa533ddc5e6b72"],"state_sha256":"1845afee6cc047ff1cb157f0f03665619418b2d021065ed269e4a278255e43d4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sxv6X5KZX0NhMWCl5gYPQJqili9xVOaO7TeLtrJ0iLeZLHWAaH60GKBoUl4scuT4QvJTDDh+3o/xevywjyT+Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T18:31:23.666844Z","bundle_sha256":"f7717a0067f3f1fa29f0b9638e50f96eb17e9eb34b41475d8e5d838fa9427d05"}}