{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:K373Y4NBZIZUJ3IYDFU7M2XSDP","short_pith_number":"pith:K373Y4NB","canonical_record":{"source":{"id":"1711.02766","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2017-11-07T23:20:49Z","cross_cats_sorted":[],"title_canon_sha256":"a13d0c12c3ae471eeb9439881c6c52df22108b29e92d8c6a40d0e46a535579c1","abstract_canon_sha256":"f3d55bb7369a0105f40c4ccda2ac1546584226788565fa1e8e3189ac9e615394"},"schema_version":"1.0"},"canonical_sha256":"56ffbc71a1ca3344ed181969f66af21bca6a364a6a48bdd9f53607565658acd1","source":{"kind":"arxiv","id":"1711.02766","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.02766","created_at":"2026-05-17T23:42:53Z"},{"alias_kind":"arxiv_version","alias_value":"1711.02766v3","created_at":"2026-05-17T23:42:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.02766","created_at":"2026-05-17T23:42:53Z"},{"alias_kind":"pith_short_12","alias_value":"K373Y4NBZIZU","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"K373Y4NBZIZUJ3IY","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"K373Y4NB","created_at":"2026-05-18T12:31:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:K373Y4NBZIZUJ3IYDFU7M2XSDP","target":"record","payload":{"canonical_record":{"source":{"id":"1711.02766","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2017-11-07T23:20:49Z","cross_cats_sorted":[],"title_canon_sha256":"a13d0c12c3ae471eeb9439881c6c52df22108b29e92d8c6a40d0e46a535579c1","abstract_canon_sha256":"f3d55bb7369a0105f40c4ccda2ac1546584226788565fa1e8e3189ac9e615394"},"schema_version":"1.0"},"canonical_sha256":"56ffbc71a1ca3344ed181969f66af21bca6a364a6a48bdd9f53607565658acd1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:53.951746Z","signature_b64":"Fy2oJjXFNk6LZd0wbpHi5UjqK5AEVqJ9ofVQt8xy21GfpCYeQXAO/FzZWyF6MSliCK9QoVUByGQeAnqSJbQ9DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"56ffbc71a1ca3344ed181969f66af21bca6a364a6a48bdd9f53607565658acd1","last_reissued_at":"2026-05-17T23:42:53.951097Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:53.951097Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.02766","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:42:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7rFYrIX0K0xfc057EUSu09v7rhfpQNEDUzW//oZ0tbN8JEaO4AJQwEpK5Qdd6ZIYUhmvA//rynSg6aZKrxOBBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T22:10:18.369719Z"},"content_sha256":"37535233f8f65cc3ba9a207ea824207685d85330ac2e060ad67c229fe5febb7e","schema_version":"1.0","event_id":"sha256:37535233f8f65cc3ba9a207ea824207685d85330ac2e060ad67c229fe5febb7e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:K373Y4NBZIZUJ3IYDFU7M2XSDP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Space-time random walk loop measures","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Quirin Vogel, Stefan Adams","submitted_at":"2017-11-07T23:20:49Z","abstract_excerpt":"In this work, we investigate a novel setting of Markovian loop measures and introduce a new class of loop measures called Bosonic loop measures. Namely, we consider loop soups with varying intensity $ \\mu\\le 0 $ (chemical potential in physics terms), and secondly, we study Markovian loop measures on graphs with an additional \"time\" dimension leading to so-called space-time random walks and their loop measures and Poisson point loop processes. Interesting phenomena appear when the additional coordinate of the space-time process is on a discrete torus with non-symmetric jump rates. The projectio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.02766","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-17T23:42:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fPOuU8me9QTj0s0SYWikgtkDMoJt3m+FP7lXAClkuZCxZdWC+u1EK+9gMRNI5BR4sV/t4gw/phKRLFiIx9VzAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T22:10:18.370080Z"},"content_sha256":"4fea3e8832ff2de1e1aa988f7920b5eaf13a965e9f08c6aec8f7f872f8ea12fa","schema_version":"1.0","event_id":"sha256:4fea3e8832ff2de1e1aa988f7920b5eaf13a965e9f08c6aec8f7f872f8ea12fa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K373Y4NBZIZUJ3IYDFU7M2XSDP/bundle.json","state_url":"https://pith.science/pith/K373Y4NBZIZUJ3IYDFU7M2XSDP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K373Y4NBZIZUJ3IYDFU7M2XSDP/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":"2026-05-26T22:10:18Z","links":{"resolver":"https://pith.science/pith/K373Y4NBZIZUJ3IYDFU7M2XSDP","bundle":"https://pith.science/pith/K373Y4NBZIZUJ3IYDFU7M2XSDP/bundle.json","state":"https://pith.science/pith/K373Y4NBZIZUJ3IYDFU7M2XSDP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K373Y4NBZIZUJ3IYDFU7M2XSDP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:K373Y4NBZIZUJ3IYDFU7M2XSDP","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":"f3d55bb7369a0105f40c4ccda2ac1546584226788565fa1e8e3189ac9e615394","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2017-11-07T23:20:49Z","title_canon_sha256":"a13d0c12c3ae471eeb9439881c6c52df22108b29e92d8c6a40d0e46a535579c1"},"schema_version":"1.0","source":{"id":"1711.02766","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.02766","created_at":"2026-05-17T23:42:53Z"},{"alias_kind":"arxiv_version","alias_value":"1711.02766v3","created_at":"2026-05-17T23:42:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.02766","created_at":"2026-05-17T23:42:53Z"},{"alias_kind":"pith_short_12","alias_value":"K373Y4NBZIZU","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"K373Y4NBZIZUJ3IY","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"K373Y4NB","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:4fea3e8832ff2de1e1aa988f7920b5eaf13a965e9f08c6aec8f7f872f8ea12fa","target":"graph","created_at":"2026-05-17T23:42:53Z","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"},"paper":{"abstract_excerpt":"In this work, we investigate a novel setting of Markovian loop measures and introduce a new class of loop measures called Bosonic loop measures. Namely, we consider loop soups with varying intensity $ \\mu\\le 0 $ (chemical potential in physics terms), and secondly, we study Markovian loop measures on graphs with an additional \"time\" dimension leading to so-called space-time random walks and their loop measures and Poisson point loop processes. Interesting phenomena appear when the additional coordinate of the space-time process is on a discrete torus with non-symmetric jump rates. The projectio","authors_text":"Quirin Vogel, Stefan Adams","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2017-11-07T23:20:49Z","title":"Space-time random walk loop measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.02766","kind":"arxiv","version":3},"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":"sha256:37535233f8f65cc3ba9a207ea824207685d85330ac2e060ad67c229fe5febb7e","target":"record","created_at":"2026-05-17T23:42:53Z","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":"f3d55bb7369a0105f40c4ccda2ac1546584226788565fa1e8e3189ac9e615394","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2017-11-07T23:20:49Z","title_canon_sha256":"a13d0c12c3ae471eeb9439881c6c52df22108b29e92d8c6a40d0e46a535579c1"},"schema_version":"1.0","source":{"id":"1711.02766","kind":"arxiv","version":3}},"canonical_sha256":"56ffbc71a1ca3344ed181969f66af21bca6a364a6a48bdd9f53607565658acd1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"56ffbc71a1ca3344ed181969f66af21bca6a364a6a48bdd9f53607565658acd1","first_computed_at":"2026-05-17T23:42:53.951097Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:53.951097Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Fy2oJjXFNk6LZd0wbpHi5UjqK5AEVqJ9ofVQt8xy21GfpCYeQXAO/FzZWyF6MSliCK9QoVUByGQeAnqSJbQ9DQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:53.951746Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.02766","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:37535233f8f65cc3ba9a207ea824207685d85330ac2e060ad67c229fe5febb7e","sha256:4fea3e8832ff2de1e1aa988f7920b5eaf13a965e9f08c6aec8f7f872f8ea12fa"],"state_sha256":"b51002c424fb62a4ecd86017f73cb03a0acdfc92f691830a0845810bc56043ad"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QHlLN8Whdr7nECXe8wXgpzMeAZTEffMcvIbJ9NW3urQEskUHTslSSqRE6gIUrQxvYhHMzVz9Thpfo0f/Be+SAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T22:10:18.372327Z","bundle_sha256":"6e0c35163f7229a954aa0d8cd84d95a3ee553a9dd73c58b558937ff8fd1106a1"}}