{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:K54TRNO7D7X7JBHDYPJJOZ3OFN","short_pith_number":"pith:K54TRNO7","canonical_record":{"source":{"id":"1512.00280","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-12-01T15:03:07Z","cross_cats_sorted":["cond-mat.stat-mech","math.CO"],"title_canon_sha256":"d24491ae7106929d9b9a4bd06b4335ad0eeb15310e81800ecff832f51f36463c","abstract_canon_sha256":"5f2fd9237ef7ad479fc3be8408e8bfec6488f96778a90a5eb9a8bdb28b498f49"},"schema_version":"1.0"},"canonical_sha256":"577938b5df1feff484e3c3d297676e2b7741c7aec0381b8f2e2db52b4873f532","source":{"kind":"arxiv","id":"1512.00280","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.00280","created_at":"2026-05-18T01:11:57Z"},{"alias_kind":"arxiv_version","alias_value":"1512.00280v2","created_at":"2026-05-18T01:11:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.00280","created_at":"2026-05-18T01:11:57Z"},{"alias_kind":"pith_short_12","alias_value":"K54TRNO7D7X7","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"K54TRNO7D7X7JBHD","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"K54TRNO7","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:K54TRNO7D7X7JBHDYPJJOZ3OFN","target":"record","payload":{"canonical_record":{"source":{"id":"1512.00280","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-12-01T15:03:07Z","cross_cats_sorted":["cond-mat.stat-mech","math.CO"],"title_canon_sha256":"d24491ae7106929d9b9a4bd06b4335ad0eeb15310e81800ecff832f51f36463c","abstract_canon_sha256":"5f2fd9237ef7ad479fc3be8408e8bfec6488f96778a90a5eb9a8bdb28b498f49"},"schema_version":"1.0"},"canonical_sha256":"577938b5df1feff484e3c3d297676e2b7741c7aec0381b8f2e2db52b4873f532","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:57.732213Z","signature_b64":"gSpUlJkvCJCj0CLinOp3F7HaPgW/eSqLoJUjhWKXRdlJJpe01U+PwK1Bi/H/9u7O7sT6MmuvopMhcxv3Og49Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"577938b5df1feff484e3c3d297676e2b7741c7aec0381b8f2e2db52b4873f532","last_reissued_at":"2026-05-18T01:11:57.731753Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:57.731753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.00280","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:11:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+duHbnhETunBskTu8zO86UrBRkYTh1RUvPGWCIii7IHM9jifWBVz1Inbr3n+E84rkg5EoqGnMuatZV6mzSBKDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T17:01:49.744487Z"},"content_sha256":"201781e6d9a5576e5e642acbeb534a37e9c04c02c95f5ca8480be65ee3faf12a","schema_version":"1.0","event_id":"sha256:201781e6d9a5576e5e642acbeb534a37e9c04c02c95f5ca8480be65ee3faf12a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:K54TRNO7D7X7JBHDYPJJOZ3OFN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spiral Structures in the Rotor-Router Walk","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.CO"],"primary_cat":"math.PR","authors_text":"V.B. Priezzhev, Vl.V. Papoyan, V.S. Poghosyan","submitted_at":"2015-12-01T15:03:07Z","abstract_excerpt":"We study the rotor-router walk on the infinite square lattice with the outgoing edges at each lattice site ordered clockwise. In the previous paper [J.Phys.A: Math. Theor. 48, 285203 (2015)], we have considered the loops created by rotors and labeled sites where the loops become closed. The sequence of labels in the rotor-router walk was conjectured to form a spiral structure obeying asymptotically an Archimedean property. In the present paper, we select a subset of labels called \"nodes\" and consider spirals formed by nodes. The new spirals are directly related to tree-like structures which re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00280","kind":"arxiv","version":2},"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":"2026-05-18T01:11:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QAGdQsSyvos+tGOzjkaZwXXWHvoLQ35vzY/KpewAzs/hO51lOBVAlK14X5eLW2Lmo0uu3AYC/nPnZD5G+Nk4CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T17:01:49.745309Z"},"content_sha256":"c6c410a0579ddf4737b10fa211d6683d66086bbdb7ee4ffa580c681f95bdda96","schema_version":"1.0","event_id":"sha256:c6c410a0579ddf4737b10fa211d6683d66086bbdb7ee4ffa580c681f95bdda96"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K54TRNO7D7X7JBHDYPJJOZ3OFN/bundle.json","state_url":"https://pith.science/pith/K54TRNO7D7X7JBHDYPJJOZ3OFN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K54TRNO7D7X7JBHDYPJJOZ3OFN/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":"2026-06-08T17:01:49Z","links":{"resolver":"https://pith.science/pith/K54TRNO7D7X7JBHDYPJJOZ3OFN","bundle":"https://pith.science/pith/K54TRNO7D7X7JBHDYPJJOZ3OFN/bundle.json","state":"https://pith.science/pith/K54TRNO7D7X7JBHDYPJJOZ3OFN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K54TRNO7D7X7JBHDYPJJOZ3OFN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:K54TRNO7D7X7JBHDYPJJOZ3OFN","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":"5f2fd9237ef7ad479fc3be8408e8bfec6488f96778a90a5eb9a8bdb28b498f49","cross_cats_sorted":["cond-mat.stat-mech","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-12-01T15:03:07Z","title_canon_sha256":"d24491ae7106929d9b9a4bd06b4335ad0eeb15310e81800ecff832f51f36463c"},"schema_version":"1.0","source":{"id":"1512.00280","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.00280","created_at":"2026-05-18T01:11:57Z"},{"alias_kind":"arxiv_version","alias_value":"1512.00280v2","created_at":"2026-05-18T01:11:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.00280","created_at":"2026-05-18T01:11:57Z"},{"alias_kind":"pith_short_12","alias_value":"K54TRNO7D7X7","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"K54TRNO7D7X7JBHD","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"K54TRNO7","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:c6c410a0579ddf4737b10fa211d6683d66086bbdb7ee4ffa580c681f95bdda96","target":"graph","created_at":"2026-05-18T01:11:57Z","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":"We study the rotor-router walk on the infinite square lattice with the outgoing edges at each lattice site ordered clockwise. In the previous paper [J.Phys.A: Math. Theor. 48, 285203 (2015)], we have considered the loops created by rotors and labeled sites where the loops become closed. The sequence of labels in the rotor-router walk was conjectured to form a spiral structure obeying asymptotically an Archimedean property. In the present paper, we select a subset of labels called \"nodes\" and consider spirals formed by nodes. The new spirals are directly related to tree-like structures which re","authors_text":"V.B. Priezzhev, Vl.V. Papoyan, V.S. Poghosyan","cross_cats":["cond-mat.stat-mech","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-12-01T15:03:07Z","title":"Spiral Structures in the Rotor-Router Walk"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00280","kind":"arxiv","version":2},"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":"sha256:201781e6d9a5576e5e642acbeb534a37e9c04c02c95f5ca8480be65ee3faf12a","target":"record","created_at":"2026-05-18T01:11:57Z","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":"5f2fd9237ef7ad479fc3be8408e8bfec6488f96778a90a5eb9a8bdb28b498f49","cross_cats_sorted":["cond-mat.stat-mech","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-12-01T15:03:07Z","title_canon_sha256":"d24491ae7106929d9b9a4bd06b4335ad0eeb15310e81800ecff832f51f36463c"},"schema_version":"1.0","source":{"id":"1512.00280","kind":"arxiv","version":2}},"canonical_sha256":"577938b5df1feff484e3c3d297676e2b7741c7aec0381b8f2e2db52b4873f532","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"577938b5df1feff484e3c3d297676e2b7741c7aec0381b8f2e2db52b4873f532","first_computed_at":"2026-05-18T01:11:57.731753Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:57.731753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gSpUlJkvCJCj0CLinOp3F7HaPgW/eSqLoJUjhWKXRdlJJpe01U+PwK1Bi/H/9u7O7sT6MmuvopMhcxv3Og49Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:57.732213Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.00280","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:201781e6d9a5576e5e642acbeb534a37e9c04c02c95f5ca8480be65ee3faf12a","sha256:c6c410a0579ddf4737b10fa211d6683d66086bbdb7ee4ffa580c681f95bdda96"],"state_sha256":"d6d30d85c235b8a8d14eb520b6e1ff1a890d1143ffaf48978af7eb63b1881e9b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YwqhmOd/oQyTdMwklws9WNCRY/vdEXjS2WExtxB7mjTACfGXu1XIiOZ1yCgaU9gNQA2LkPTSej6V3ub1cQTJAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T17:01:49.749412Z","bundle_sha256":"983b871c139588ec56e7716807b3a77a37715f62694a52bc8e7944c040c535c4"}}