{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:5DAFP6RQ3THLPEC3YQDUG5AXOV","short_pith_number":"pith:5DAFP6RQ","canonical_record":{"source":{"id":"2607.08128","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2026-07-09T05:56:53Z","cross_cats_sorted":[],"title_canon_sha256":"eb114528c16c415fb922143d0f091a1cae974d1f608d849cd1bbed3046436be8","abstract_canon_sha256":"09c0fd8252376847c0150a4dfc05993d07f4a408aae7041f32bb8cc81fce2056"},"schema_version":"1.0"},"canonical_sha256":"e8c057fa30dcceb7905bc407437417756a48c12bd46e3ed22da2488529aa09cc","source":{"kind":"arxiv","id":"2607.08128","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.08128","created_at":"2026-07-10T01:19:27Z"},{"alias_kind":"arxiv_version","alias_value":"2607.08128v1","created_at":"2026-07-10T01:19:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.08128","created_at":"2026-07-10T01:19:27Z"},{"alias_kind":"pith_short_12","alias_value":"5DAFP6RQ3THL","created_at":"2026-07-10T01:19:27Z"},{"alias_kind":"pith_short_16","alias_value":"5DAFP6RQ3THLPEC3","created_at":"2026-07-10T01:19:27Z"},{"alias_kind":"pith_short_8","alias_value":"5DAFP6RQ","created_at":"2026-07-10T01:19:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:5DAFP6RQ3THLPEC3YQDUG5AXOV","target":"record","payload":{"canonical_record":{"source":{"id":"2607.08128","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2026-07-09T05:56:53Z","cross_cats_sorted":[],"title_canon_sha256":"eb114528c16c415fb922143d0f091a1cae974d1f608d849cd1bbed3046436be8","abstract_canon_sha256":"09c0fd8252376847c0150a4dfc05993d07f4a408aae7041f32bb8cc81fce2056"},"schema_version":"1.0"},"canonical_sha256":"e8c057fa30dcceb7905bc407437417756a48c12bd46e3ed22da2488529aa09cc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-10T01:19:27.431179Z","signature_b64":"9zyMWKYpAVrz+odF1IJFNfPQeUkGAlAWazqdqdJoCSJQQT8pe1QMmw8DeHCq9unWtPe/NexoyXGonIh6V06WBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8c057fa30dcceb7905bc407437417756a48c12bd46e3ed22da2488529aa09cc","last_reissued_at":"2026-07-10T01:19:27.430749Z","signature_status":"signed_v1","first_computed_at":"2026-07-10T01:19:27.430749Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.08128","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":"2026-07-10T01:19:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zcgemPOxQiyZLuLgpAel+PTDeKbB2z++UNfs+E+4oKmWCvDyh83alVsgdm3mXHzRmixAIhV1hRVsdAnHWuF8BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T17:10:54.735937Z"},"content_sha256":"3f24d18faf48c9ce40179510b6ca5c634e873ed3eb1c776feeb07a87fd4a32c9","schema_version":"1.0","event_id":"sha256:3f24d18faf48c9ce40179510b6ca5c634e873ed3eb1c776feeb07a87fd4a32c9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:5DAFP6RQ3THLPEC3YQDUG5AXOV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Survey on Multiset Dimension and Its Variations","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Azzah Albejani, Joe Ryan, Kiki A. Sugeng, Yuqing Lin","submitted_at":"2026-07-09T05:56:53Z","abstract_excerpt":"The classical notion of metric dimension has led to a wide range of extensions, such as the local, strong, fractional, and k-metric dimensions. This naturally raises the question of whether analogous variants can be formulated and studied within the multiset framework. While some progress has been made, particularly on the local multiset dimension, outer multiset dimension, local outer multiset dimension, and edge multiset dimension, however, the area remains far from fully explored. In this paper, we survey the existing variants and consolidate the results currently available in the literatur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.08128","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/2607.08128/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":"2026-07-10T01:19:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cPCSJbUARWS9AwdL0I/nncek5wOPz0ojbb+EUmyEmLcO02V1ALnyDrmQaNe+5jlerFDkRKwjhb+yCRPCqasWDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T17:10:54.736624Z"},"content_sha256":"38e17a22a22292ba319c61ff4badcc9cc2b6a9f18ee395e36951cd51e1cfbb3a","schema_version":"1.0","event_id":"sha256:38e17a22a22292ba319c61ff4badcc9cc2b6a9f18ee395e36951cd51e1cfbb3a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5DAFP6RQ3THLPEC3YQDUG5AXOV/bundle.json","state_url":"https://pith.science/pith/5DAFP6RQ3THLPEC3YQDUG5AXOV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5DAFP6RQ3THLPEC3YQDUG5AXOV/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":"2026-08-08T17:10:54Z","links":{"resolver":"https://pith.science/pith/5DAFP6RQ3THLPEC3YQDUG5AXOV","bundle":"https://pith.science/pith/5DAFP6RQ3THLPEC3YQDUG5AXOV/bundle.json","state":"https://pith.science/pith/5DAFP6RQ3THLPEC3YQDUG5AXOV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5DAFP6RQ3THLPEC3YQDUG5AXOV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:5DAFP6RQ3THLPEC3YQDUG5AXOV","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":"09c0fd8252376847c0150a4dfc05993d07f4a408aae7041f32bb8cc81fce2056","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2026-07-09T05:56:53Z","title_canon_sha256":"eb114528c16c415fb922143d0f091a1cae974d1f608d849cd1bbed3046436be8"},"schema_version":"1.0","source":{"id":"2607.08128","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.08128","created_at":"2026-07-10T01:19:27Z"},{"alias_kind":"arxiv_version","alias_value":"2607.08128v1","created_at":"2026-07-10T01:19:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.08128","created_at":"2026-07-10T01:19:27Z"},{"alias_kind":"pith_short_12","alias_value":"5DAFP6RQ3THL","created_at":"2026-07-10T01:19:27Z"},{"alias_kind":"pith_short_16","alias_value":"5DAFP6RQ3THLPEC3","created_at":"2026-07-10T01:19:27Z"},{"alias_kind":"pith_short_8","alias_value":"5DAFP6RQ","created_at":"2026-07-10T01:19:27Z"}],"graph_snapshots":[{"event_id":"sha256:38e17a22a22292ba319c61ff4badcc9cc2b6a9f18ee395e36951cd51e1cfbb3a","target":"graph","created_at":"2026-07-10T01:19:27Z","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/2607.08128/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The classical notion of metric dimension has led to a wide range of extensions, such as the local, strong, fractional, and k-metric dimensions. This naturally raises the question of whether analogous variants can be formulated and studied within the multiset framework. While some progress has been made, particularly on the local multiset dimension, outer multiset dimension, local outer multiset dimension, and edge multiset dimension, however, the area remains far from fully explored. In this paper, we survey the existing variants and consolidate the results currently available in the literatur","authors_text":"Azzah Albejani, Joe Ryan, Kiki A. Sugeng, Yuqing Lin","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2026-07-09T05:56:53Z","title":"A Survey on Multiset Dimension and Its Variations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.08128","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":"sha256:3f24d18faf48c9ce40179510b6ca5c634e873ed3eb1c776feeb07a87fd4a32c9","target":"record","created_at":"2026-07-10T01:19:27Z","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":"09c0fd8252376847c0150a4dfc05993d07f4a408aae7041f32bb8cc81fce2056","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2026-07-09T05:56:53Z","title_canon_sha256":"eb114528c16c415fb922143d0f091a1cae974d1f608d849cd1bbed3046436be8"},"schema_version":"1.0","source":{"id":"2607.08128","kind":"arxiv","version":1}},"canonical_sha256":"e8c057fa30dcceb7905bc407437417756a48c12bd46e3ed22da2488529aa09cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8c057fa30dcceb7905bc407437417756a48c12bd46e3ed22da2488529aa09cc","first_computed_at":"2026-07-10T01:19:27.430749Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-10T01:19:27.430749Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9zyMWKYpAVrz+odF1IJFNfPQeUkGAlAWazqdqdJoCSJQQT8pe1QMmw8DeHCq9unWtPe/NexoyXGonIh6V06WBg==","signature_status":"signed_v1","signed_at":"2026-07-10T01:19:27.431179Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.08128","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f24d18faf48c9ce40179510b6ca5c634e873ed3eb1c776feeb07a87fd4a32c9","sha256:38e17a22a22292ba319c61ff4badcc9cc2b6a9f18ee395e36951cd51e1cfbb3a"],"state_sha256":"a51dbd0ce6a8c73ed2235a8df914182136ea2bd35416725773b4dd22200589b4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fPa6JENGLagqkSmYfzOkr9uAa/PH9sSDrF/fYf5HA82PcUkZ/qHCZ9u9ge0oonVVsDRysE7BzKG+7WFV6FVOCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T17:10:54.740756Z","bundle_sha256":"095e24c093028d82a17ebcd9388e2cfb52d449292eb4a3a92f6e524f1a377fd6"}}